3 C<isl> is a thread-safe C library for manipulating
4 sets and relations of integer points bounded by affine constraints.
5 The descriptions of the sets and relations may involve
6 both parameters and existentially quantified variables.
7 All computations are performed in exact integer arithmetic
9 The C<isl> library offers functionality that is similar
10 to that offered by the C<Omega> and C<Omega+> libraries,
11 but the underlying algorithms are in most cases completely different.
13 The library is by no means complete and some fairly basic
14 functionality is still missing.
15 Still, even in its current form, the library has been successfully
16 used as a backend polyhedral library for the polyhedral
17 scanner C<CLooG> and as part of an equivalence checker of
18 static affine programs.
19 For bug reports, feature requests and questions,
20 visit the the discussion group at
21 L<http://groups.google.com/group/isl-development>.
23 =head2 Backward Incompatible Changes
25 =head3 Changes since isl-0.02
29 =item * The old printing functions have been deprecated
30 and replaced by C<isl_printer> functions, see L<Input and Output>.
32 =item * Most functions related to dependence analysis have acquired
33 an extra C<must> argument. To obtain the old behavior, this argument
34 should be given the value 1. See L<Dependence Analysis>.
38 =head3 Changes since isl-0.03
42 =item * The function C<isl_pw_qpolynomial_fold_add> has been
43 renamed to C<isl_pw_qpolynomial_fold_fold>.
44 Similarly, C<isl_union_pw_qpolynomial_fold_add> has been
45 renamed to C<isl_union_pw_qpolynomial_fold_fold>.
49 =head3 Changes since isl-0.04
53 =item * All header files have been renamed from C<isl_header.h>
58 =head3 Changes since isl-0.05
62 =item * The functions C<isl_printer_print_basic_set> and
63 C<isl_printer_print_basic_map> no longer print a newline.
65 =item * The functions C<isl_flow_get_no_source>
66 and C<isl_union_map_compute_flow> now return
67 the accesses for which no source could be found instead of
68 the iterations where those accesses occur.
70 =item * The functions C<isl_basic_map_identity> and
71 C<isl_map_identity> now take the dimension specification
72 of a B<map> as input. An old call
73 C<isl_map_identity(dim)> can be rewritten to
74 C<isl_map_identity(isl_dim_map_from_set(dim))>.
76 =item * The function C<isl_map_power> no longer takes
77 a parameter position as input. Instead, the exponent
78 is now expressed as the domain of the resulting relation.
82 =head3 Changes since isl-0.06
86 =item * The format of C<isl_printer_print_qpolynomial>'s
87 C<ISL_FORMAT_ISL> output has changed.
88 Use C<ISL_FORMAT_C> to obtain the old output.
94 The source of C<isl> can be obtained either as a tarball
95 or from the git repository. Both are available from
96 L<http://freshmeat.net/projects/isl/>.
97 The installation process depends on how you obtained
100 =head2 Installation from the git repository
104 =item 1 Clone or update the repository
106 The first time the source is obtained, you need to clone
109 git clone git://repo.or.cz/isl.git
111 To obtain updates, you need to pull in the latest changes
115 =item 2 Generate C<configure>
121 After performing the above steps, continue
122 with the L<Common installation instructions>.
124 =head2 Common installation instructions
128 =item 1 Obtain C<GMP>
130 Building C<isl> requires C<GMP>, including its headers files.
131 Your distribution may not provide these header files by default
132 and you may need to install a package called C<gmp-devel> or something
133 similar. Alternatively, C<GMP> can be built from
134 source, available from L<http://gmplib.org/>.
138 C<isl> uses the standard C<autoconf> C<configure> script.
143 optionally followed by some configure options.
144 A complete list of options can be obtained by running
148 Below we discuss some of the more common options.
150 C<isl> can optionally use C<piplib>, but no
151 C<piplib> functionality is currently used by default.
152 The C<--with-piplib> option can
153 be used to specify which C<piplib>
154 library to use, either an installed version (C<system>),
155 an externally built version (C<build>)
156 or no version (C<no>). The option C<build> is mostly useful
157 in C<configure> scripts of larger projects that bundle both C<isl>
164 Installation prefix for C<isl>
166 =item C<--with-gmp-prefix>
168 Installation prefix for C<GMP> (architecture-independent files).
170 =item C<--with-gmp-exec-prefix>
172 Installation prefix for C<GMP> (architecture-dependent files).
174 =item C<--with-piplib>
176 Which copy of C<piplib> to use, either C<no> (default), C<system> or C<build>.
178 =item C<--with-piplib-prefix>
180 Installation prefix for C<system> C<piplib> (architecture-independent files).
182 =item C<--with-piplib-exec-prefix>
184 Installation prefix for C<system> C<piplib> (architecture-dependent files).
186 =item C<--with-piplib-builddir>
188 Location where C<build> C<piplib> was built.
196 =item 4 Install (optional)
204 =head2 Initialization
206 All manipulations of integer sets and relations occur within
207 the context of an C<isl_ctx>.
208 A given C<isl_ctx> can only be used within a single thread.
209 All arguments of a function are required to have been allocated
210 within the same context.
211 There are currently no functions available for moving an object
212 from one C<isl_ctx> to another C<isl_ctx>. This means that
213 there is currently no way of safely moving an object from one
214 thread to another, unless the whole C<isl_ctx> is moved.
216 An C<isl_ctx> can be allocated using C<isl_ctx_alloc> and
217 freed using C<isl_ctx_free>.
218 All objects allocated within an C<isl_ctx> should be freed
219 before the C<isl_ctx> itself is freed.
221 isl_ctx *isl_ctx_alloc();
222 void isl_ctx_free(isl_ctx *ctx);
226 All operations on integers, mainly the coefficients
227 of the constraints describing the sets and relations,
228 are performed in exact integer arithmetic using C<GMP>.
229 However, to allow future versions of C<isl> to optionally
230 support fixed integer arithmetic, all calls to C<GMP>
231 are wrapped inside C<isl> specific macros.
232 The basic type is C<isl_int> and the operations below
233 are available on this type.
234 The meanings of these operations are essentially the same
235 as their C<GMP> C<mpz_> counterparts.
236 As always with C<GMP> types, C<isl_int>s need to be
237 initialized with C<isl_int_init> before they can be used
238 and they need to be released with C<isl_int_clear>
240 The user should not assume that an C<isl_int> is represented
241 as a C<mpz_t>, but should instead explicitly convert between
242 C<mpz_t>s and C<isl_int>s using C<isl_int_set_gmp> and
243 C<isl_int_get_gmp> whenever a C<mpz_t> is required.
247 =item isl_int_init(i)
249 =item isl_int_clear(i)
251 =item isl_int_set(r,i)
253 =item isl_int_set_si(r,i)
255 =item isl_int_set_gmp(r,g)
257 =item isl_int_get_gmp(i,g)
259 =item isl_int_abs(r,i)
261 =item isl_int_neg(r,i)
263 =item isl_int_swap(i,j)
265 =item isl_int_swap_or_set(i,j)
267 =item isl_int_add_ui(r,i,j)
269 =item isl_int_sub_ui(r,i,j)
271 =item isl_int_add(r,i,j)
273 =item isl_int_sub(r,i,j)
275 =item isl_int_mul(r,i,j)
277 =item isl_int_mul_ui(r,i,j)
279 =item isl_int_addmul(r,i,j)
281 =item isl_int_submul(r,i,j)
283 =item isl_int_gcd(r,i,j)
285 =item isl_int_lcm(r,i,j)
287 =item isl_int_divexact(r,i,j)
289 =item isl_int_cdiv_q(r,i,j)
291 =item isl_int_fdiv_q(r,i,j)
293 =item isl_int_fdiv_r(r,i,j)
295 =item isl_int_fdiv_q_ui(r,i,j)
297 =item isl_int_read(r,s)
299 =item isl_int_print(out,i,width)
303 =item isl_int_cmp(i,j)
305 =item isl_int_cmp_si(i,si)
307 =item isl_int_eq(i,j)
309 =item isl_int_ne(i,j)
311 =item isl_int_lt(i,j)
313 =item isl_int_le(i,j)
315 =item isl_int_gt(i,j)
317 =item isl_int_ge(i,j)
319 =item isl_int_abs_eq(i,j)
321 =item isl_int_abs_ne(i,j)
323 =item isl_int_abs_lt(i,j)
325 =item isl_int_abs_gt(i,j)
327 =item isl_int_abs_ge(i,j)
329 =item isl_int_is_zero(i)
331 =item isl_int_is_one(i)
333 =item isl_int_is_negone(i)
335 =item isl_int_is_pos(i)
337 =item isl_int_is_neg(i)
339 =item isl_int_is_nonpos(i)
341 =item isl_int_is_nonneg(i)
343 =item isl_int_is_divisible_by(i,j)
347 =head2 Sets and Relations
349 C<isl> uses six types of objects for representing sets and relations,
350 C<isl_basic_set>, C<isl_basic_map>, C<isl_set>, C<isl_map>,
351 C<isl_union_set> and C<isl_union_map>.
352 C<isl_basic_set> and C<isl_basic_map> represent sets and relations that
353 can be described as a conjunction of affine constraints, while
354 C<isl_set> and C<isl_map> represent unions of
355 C<isl_basic_set>s and C<isl_basic_map>s, respectively.
356 However, all C<isl_basic_set>s or C<isl_basic_map>s in the union need
357 to have the same dimension. C<isl_union_set>s and C<isl_union_map>s
358 represent unions of C<isl_set>s or C<isl_map>s of I<different> dimensions,
359 where dimensions with different space names
360 (see L<Dimension Specifications>) are considered different as well.
361 The difference between sets and relations (maps) is that sets have
362 one set of variables, while relations have two sets of variables,
363 input variables and output variables.
365 =head2 Memory Management
367 Since a high-level operation on sets and/or relations usually involves
368 several substeps and since the user is usually not interested in
369 the intermediate results, most functions that return a new object
370 will also release all the objects passed as arguments.
371 If the user still wants to use one or more of these arguments
372 after the function call, she should pass along a copy of the
373 object rather than the object itself.
374 The user is then responsible for making sure that the original
375 object gets used somewhere else or is explicitly freed.
377 The arguments and return values of all documents functions are
378 annotated to make clear which arguments are released and which
379 arguments are preserved. In particular, the following annotations
386 C<__isl_give> means that a new object is returned.
387 The user should make sure that the returned pointer is
388 used exactly once as a value for an C<__isl_take> argument.
389 In between, it can be used as a value for as many
390 C<__isl_keep> arguments as the user likes.
391 There is one exception, and that is the case where the
392 pointer returned is C<NULL>. Is this case, the user
393 is free to use it as an C<__isl_take> argument or not.
397 C<__isl_take> means that the object the argument points to
398 is taken over by the function and may no longer be used
399 by the user as an argument to any other function.
400 The pointer value must be one returned by a function
401 returning an C<__isl_give> pointer.
402 If the user passes in a C<NULL> value, then this will
403 be treated as an error in the sense that the function will
404 not perform its usual operation. However, it will still
405 make sure that all the the other C<__isl_take> arguments
410 C<__isl_keep> means that the function will only use the object
411 temporarily. After the function has finished, the user
412 can still use it as an argument to other functions.
413 A C<NULL> value will be treated in the same way as
414 a C<NULL> value for an C<__isl_take> argument.
418 =head2 Dimension Specifications
420 Whenever a new set or relation is created from scratch,
421 its dimension needs to be specified using an C<isl_dim>.
424 __isl_give isl_dim *isl_dim_alloc(isl_ctx *ctx,
425 unsigned nparam, unsigned n_in, unsigned n_out);
426 __isl_give isl_dim *isl_dim_set_alloc(isl_ctx *ctx,
427 unsigned nparam, unsigned dim);
428 __isl_give isl_dim *isl_dim_copy(__isl_keep isl_dim *dim);
429 void isl_dim_free(__isl_take isl_dim *dim);
430 unsigned isl_dim_size(__isl_keep isl_dim *dim,
431 enum isl_dim_type type);
433 The dimension specification used for creating a set
434 needs to be created using C<isl_dim_set_alloc>, while
435 that for creating a relation
436 needs to be created using C<isl_dim_alloc>.
437 C<isl_dim_size> can be used
438 to find out the number of dimensions of each type in
439 a dimension specification, where type may be
440 C<isl_dim_param>, C<isl_dim_in> (only for relations),
441 C<isl_dim_out> (only for relations), C<isl_dim_set>
442 (only for sets) or C<isl_dim_all>.
444 It is often useful to create objects that live in the
445 same space as some other object. This can be accomplished
446 by creating the new objects
447 (see L<Creating New Sets and Relations> or
448 L<Creating New (Piecewise) Quasipolynomials>) based on the dimension
449 specification of the original object.
452 __isl_give isl_dim *isl_basic_set_get_dim(
453 __isl_keep isl_basic_set *bset);
454 __isl_give isl_dim *isl_set_get_dim(__isl_keep isl_set *set);
456 #include <isl/union_set.h>
457 __isl_give isl_dim *isl_union_set_get_dim(
458 __isl_keep isl_union_set *uset);
461 __isl_give isl_dim *isl_basic_map_get_dim(
462 __isl_keep isl_basic_map *bmap);
463 __isl_give isl_dim *isl_map_get_dim(__isl_keep isl_map *map);
465 #include <isl/union_map.h>
466 __isl_give isl_dim *isl_union_map_get_dim(
467 __isl_keep isl_union_map *umap);
469 #include <isl/constraint.h>
470 __isl_give isl_dim *isl_constraint_get_dim(
471 __isl_keep isl_constraint *constraint);
473 #include <isl/polynomial.h>
474 __isl_give isl_dim *isl_qpolynomial_get_dim(
475 __isl_keep isl_qpolynomial *qp);
476 __isl_give isl_dim *isl_pw_qpolynomial_get_dim(
477 __isl_keep isl_pw_qpolynomial *pwqp);
478 __isl_give isl_dim *isl_union_pw_qpolynomial_get_dim(
479 __isl_keep isl_union_pw_qpolynomial *upwqp);
480 __isl_give isl_dim *isl_union_pw_qpolynomial_fold_get_dim(
481 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
484 __isl_give isl_dim *isl_aff_get_dim(
485 __isl_keep isl_aff *aff);
487 The names of the individual dimensions may be set or read off
488 using the following functions.
491 __isl_give isl_dim *isl_dim_set_name(__isl_take isl_dim *dim,
492 enum isl_dim_type type, unsigned pos,
493 __isl_keep const char *name);
494 __isl_keep const char *isl_dim_get_name(__isl_keep isl_dim *dim,
495 enum isl_dim_type type, unsigned pos);
497 Note that C<isl_dim_get_name> returns a pointer to some internal
498 data structure, so the result can only be used while the
499 corresponding C<isl_dim> is alive.
500 Also note that every function that operates on two sets or relations
501 requires that both arguments have the same parameters. This also
502 means that if one of the arguments has named parameters, then the
503 other needs to have named parameters too and the names need to match.
504 Pairs of C<isl_union_set> and/or C<isl_union_map> arguments may
505 have different parameters (as long as they are named), in which case
506 the result will have as parameters the union of the parameters of
509 The names of entire spaces may be set or read off
510 using the following functions.
513 __isl_give isl_dim *isl_dim_set_tuple_name(
514 __isl_take isl_dim *dim,
515 enum isl_dim_type type, const char *s);
516 const char *isl_dim_get_tuple_name(__isl_keep isl_dim *dim,
517 enum isl_dim_type type);
519 The C<dim> argument needs to be one of C<isl_dim_in>, C<isl_dim_out>
520 or C<isl_dim_set>. As with C<isl_dim_get_name>,
521 the C<isl_dim_get_tuple_name> function returns a pointer to some internal
523 Binary operations require the corresponding spaces of their arguments
524 to have the same name.
526 Spaces can be nested. In particular, the domain of a set or
527 the domain or range of a relation can be a nested relation.
528 The following functions can be used to construct and deconstruct
529 such nested dimension specifications.
532 int isl_dim_is_wrapping(__isl_keep isl_dim *dim);
533 __isl_give isl_dim *isl_dim_wrap(__isl_take isl_dim *dim);
534 __isl_give isl_dim *isl_dim_unwrap(__isl_take isl_dim *dim);
536 The input to C<isl_dim_is_wrapping> and C<isl_dim_unwrap> should
537 be the dimension specification of a set, while that of
538 C<isl_dim_wrap> should be the dimension specification of a relation.
539 Conversely, the output of C<isl_dim_unwrap> is the dimension specification
540 of a relation, while that of C<isl_dim_wrap> is the dimension specification
543 Dimension specifications can be created from other dimension
544 specifications using the following functions.
546 __isl_give isl_dim *isl_dim_domain(__isl_take isl_dim *dim);
547 __isl_give isl_dim *isl_dim_from_domain(__isl_take isl_dim *dim);
548 __isl_give isl_dim *isl_dim_range(__isl_take isl_dim *dim);
549 __isl_give isl_dim *isl_dim_from_range(__isl_take isl_dim *dim);
550 __isl_give isl_dim *isl_dim_reverse(__isl_take isl_dim *dim);
551 __isl_give isl_dim *isl_dim_join(__isl_take isl_dim *left,
552 __isl_take isl_dim *right);
553 __isl_give isl_dim *isl_dim_align_params(
554 __isl_take isl_dim *dim1, __isl_take isl_dim *dim2)
555 __isl_give isl_dim *isl_dim_insert(__isl_take isl_dim *dim,
556 enum isl_dim_type type, unsigned pos, unsigned n);
557 __isl_give isl_dim *isl_dim_add(__isl_take isl_dim *dim,
558 enum isl_dim_type type, unsigned n);
559 __isl_give isl_dim *isl_dim_drop(__isl_take isl_dim *dim,
560 enum isl_dim_type type, unsigned first, unsigned n);
561 __isl_give isl_dim *isl_dim_map_from_set(
562 __isl_take isl_dim *dim);
563 __isl_give isl_dim *isl_dim_zip(__isl_take isl_dim *dim);
565 Note that if dimensions are added or removed from a space, then
566 the name and the internal structure are lost.
570 A local space is essentially a dimension specification with
571 zero or more existentially quantified variables.
572 The local space of a basic set or relation can be obtained
573 using the following functions.
576 __isl_give isl_local_space *isl_basic_set_get_local_space(
577 __isl_keep isl_basic_set *bset);
580 __isl_give isl_local_space *isl_basic_map_get_local_space(
581 __isl_keep isl_basic_map *bmap);
583 A new local space can be created from a dimension specification using
585 #include <isl/local_space.h>
586 __isl_give isl_local_space *isl_local_space_from_dim(
587 __isl_take isl_dim *dim);
589 They can be inspected, copied and freed using the following functions.
591 #include <isl/local_space.h>
592 isl_ctx *isl_local_space_get_ctx(
593 __isl_keep isl_local_space *ls);
594 int isl_local_space_dim(__isl_keep isl_local_space *ls,
595 enum isl_dim_type type);
596 const char *isl_local_space_get_dim_name(
597 __isl_keep isl_local_space *ls,
598 enum isl_dim_type type, unsigned pos);
599 __isl_give isl_dim *isl_local_space_get_dim(
600 __isl_keep isl_local_space *ls);
601 __isl_give isl_div *isl_local_space_get_div(
602 __isl_keep isl_local_space *ls, int pos);
603 __isl_give isl_local_space *isl_local_space_copy(
604 __isl_keep isl_local_space *ls);
605 void *isl_local_space_free(__isl_take isl_local_space *ls);
607 =head2 Input and Output
609 C<isl> supports its own input/output format, which is similar
610 to the C<Omega> format, but also supports the C<PolyLib> format
615 The C<isl> format is similar to that of C<Omega>, but has a different
616 syntax for describing the parameters and allows for the definition
617 of an existentially quantified variable as the integer division
618 of an affine expression.
619 For example, the set of integers C<i> between C<0> and C<n>
620 such that C<i % 10 <= 6> can be described as
622 [n] -> { [i] : exists (a = [i/10] : 0 <= i and i <= n and
625 A set or relation can have several disjuncts, separated
626 by the keyword C<or>. Each disjunct is either a conjunction
627 of constraints or a projection (C<exists>) of a conjunction
628 of constraints. The constraints are separated by the keyword
631 =head3 C<PolyLib> format
633 If the represented set is a union, then the first line
634 contains a single number representing the number of disjuncts.
635 Otherwise, a line containing the number C<1> is optional.
637 Each disjunct is represented by a matrix of constraints.
638 The first line contains two numbers representing
639 the number of rows and columns,
640 where the number of rows is equal to the number of constraints
641 and the number of columns is equal to two plus the number of variables.
642 The following lines contain the actual rows of the constraint matrix.
643 In each row, the first column indicates whether the constraint
644 is an equality (C<0>) or inequality (C<1>). The final column
645 corresponds to the constant term.
647 If the set is parametric, then the coefficients of the parameters
648 appear in the last columns before the constant column.
649 The coefficients of any existentially quantified variables appear
650 between those of the set variables and those of the parameters.
652 =head3 Extended C<PolyLib> format
654 The extended C<PolyLib> format is nearly identical to the
655 C<PolyLib> format. The only difference is that the line
656 containing the number of rows and columns of a constraint matrix
657 also contains four additional numbers:
658 the number of output dimensions, the number of input dimensions,
659 the number of local dimensions (i.e., the number of existentially
660 quantified variables) and the number of parameters.
661 For sets, the number of ``output'' dimensions is equal
662 to the number of set dimensions, while the number of ``input''
668 __isl_give isl_basic_set *isl_basic_set_read_from_file(
669 isl_ctx *ctx, FILE *input, int nparam);
670 __isl_give isl_basic_set *isl_basic_set_read_from_str(
671 isl_ctx *ctx, const char *str, int nparam);
672 __isl_give isl_set *isl_set_read_from_file(isl_ctx *ctx,
673 FILE *input, int nparam);
674 __isl_give isl_set *isl_set_read_from_str(isl_ctx *ctx,
675 const char *str, int nparam);
678 __isl_give isl_basic_map *isl_basic_map_read_from_file(
679 isl_ctx *ctx, FILE *input, int nparam);
680 __isl_give isl_basic_map *isl_basic_map_read_from_str(
681 isl_ctx *ctx, const char *str, int nparam);
682 __isl_give isl_map *isl_map_read_from_file(
683 struct isl_ctx *ctx, FILE *input, int nparam);
684 __isl_give isl_map *isl_map_read_from_str(isl_ctx *ctx,
685 const char *str, int nparam);
687 #include <isl/union_set.h>
688 __isl_give isl_union_set *isl_union_set_read_from_file(
689 isl_ctx *ctx, FILE *input);
690 __isl_give isl_union_set *isl_union_set_read_from_str(
691 struct isl_ctx *ctx, const char *str);
693 #include <isl/union_map.h>
694 __isl_give isl_union_map *isl_union_map_read_from_file(
695 isl_ctx *ctx, FILE *input);
696 __isl_give isl_union_map *isl_union_map_read_from_str(
697 struct isl_ctx *ctx, const char *str);
699 The input format is autodetected and may be either the C<PolyLib> format
700 or the C<isl> format.
701 C<nparam> specifies how many of the final columns in
702 the C<PolyLib> format correspond to parameters.
703 If input is given in the C<isl> format, then the number
704 of parameters needs to be equal to C<nparam>.
705 If C<nparam> is negative, then any number of parameters
706 is accepted in the C<isl> format and zero parameters
707 are assumed in the C<PolyLib> format.
711 Before anything can be printed, an C<isl_printer> needs to
714 __isl_give isl_printer *isl_printer_to_file(isl_ctx *ctx,
716 __isl_give isl_printer *isl_printer_to_str(isl_ctx *ctx);
717 void isl_printer_free(__isl_take isl_printer *printer);
718 __isl_give char *isl_printer_get_str(
719 __isl_keep isl_printer *printer);
721 The behavior of the printer can be modified in various ways
723 __isl_give isl_printer *isl_printer_set_output_format(
724 __isl_take isl_printer *p, int output_format);
725 __isl_give isl_printer *isl_printer_set_indent(
726 __isl_take isl_printer *p, int indent);
727 __isl_give isl_printer *isl_printer_indent(
728 __isl_take isl_printer *p, int indent);
729 __isl_give isl_printer *isl_printer_set_prefix(
730 __isl_take isl_printer *p, const char *prefix);
731 __isl_give isl_printer *isl_printer_set_suffix(
732 __isl_take isl_printer *p, const char *suffix);
734 The C<output_format> may be either C<ISL_FORMAT_ISL>, C<ISL_FORMAT_OMEGA>,
735 C<ISL_FORMAT_POLYLIB>, C<ISL_FORMAT_EXT_POLYLIB> or C<ISL_FORMAT_LATEX>
736 and defaults to C<ISL_FORMAT_ISL>.
737 Each line in the output is indented by C<indent> (set by
738 C<isl_printer_set_indent>) spaces
739 (default: 0), prefixed by C<prefix> and suffixed by C<suffix>.
740 In the C<PolyLib> format output,
741 the coefficients of the existentially quantified variables
742 appear between those of the set variables and those
744 The function C<isl_printer_indent> increases the indentation
745 by the specified amount (which may be negative).
747 To actually print something, use
750 __isl_give isl_printer *isl_printer_print_basic_set(
751 __isl_take isl_printer *printer,
752 __isl_keep isl_basic_set *bset);
753 __isl_give isl_printer *isl_printer_print_set(
754 __isl_take isl_printer *printer,
755 __isl_keep isl_set *set);
758 __isl_give isl_printer *isl_printer_print_basic_map(
759 __isl_take isl_printer *printer,
760 __isl_keep isl_basic_map *bmap);
761 __isl_give isl_printer *isl_printer_print_map(
762 __isl_take isl_printer *printer,
763 __isl_keep isl_map *map);
765 #include <isl/union_set.h>
766 __isl_give isl_printer *isl_printer_print_union_set(
767 __isl_take isl_printer *p,
768 __isl_keep isl_union_set *uset);
770 #include <isl/union_map.h>
771 __isl_give isl_printer *isl_printer_print_union_map(
772 __isl_take isl_printer *p,
773 __isl_keep isl_union_map *umap);
775 When called on a file printer, the following function flushes
776 the file. When called on a string printer, the buffer is cleared.
778 __isl_give isl_printer *isl_printer_flush(
779 __isl_take isl_printer *p);
781 =head2 Creating New Sets and Relations
783 C<isl> has functions for creating some standard sets and relations.
787 =item * Empty sets and relations
789 __isl_give isl_basic_set *isl_basic_set_empty(
790 __isl_take isl_dim *dim);
791 __isl_give isl_basic_map *isl_basic_map_empty(
792 __isl_take isl_dim *dim);
793 __isl_give isl_set *isl_set_empty(
794 __isl_take isl_dim *dim);
795 __isl_give isl_map *isl_map_empty(
796 __isl_take isl_dim *dim);
797 __isl_give isl_union_set *isl_union_set_empty(
798 __isl_take isl_dim *dim);
799 __isl_give isl_union_map *isl_union_map_empty(
800 __isl_take isl_dim *dim);
802 For C<isl_union_set>s and C<isl_union_map>s, the dimensions specification
803 is only used to specify the parameters.
805 =item * Universe sets and relations
807 __isl_give isl_basic_set *isl_basic_set_universe(
808 __isl_take isl_dim *dim);
809 __isl_give isl_basic_map *isl_basic_map_universe(
810 __isl_take isl_dim *dim);
811 __isl_give isl_set *isl_set_universe(
812 __isl_take isl_dim *dim);
813 __isl_give isl_map *isl_map_universe(
814 __isl_take isl_dim *dim);
815 __isl_give isl_union_set *isl_union_set_universe(
816 __isl_take isl_union_set *uset);
817 __isl_give isl_union_map *isl_union_map_universe(
818 __isl_take isl_union_map *umap);
820 The sets and relations constructed by the functions above
821 contain all integer values, while those constructed by the
822 functions below only contain non-negative values.
824 __isl_give isl_basic_set *isl_basic_set_nat_universe(
825 __isl_take isl_dim *dim);
826 __isl_give isl_basic_map *isl_basic_map_nat_universe(
827 __isl_take isl_dim *dim);
828 __isl_give isl_set *isl_set_nat_universe(
829 __isl_take isl_dim *dim);
830 __isl_give isl_map *isl_map_nat_universe(
831 __isl_take isl_dim *dim);
833 =item * Identity relations
835 __isl_give isl_basic_map *isl_basic_map_identity(
836 __isl_take isl_dim *dim);
837 __isl_give isl_map *isl_map_identity(
838 __isl_take isl_dim *dim);
840 The number of input and output dimensions in C<dim> needs
843 =item * Lexicographic order
845 __isl_give isl_map *isl_map_lex_lt(
846 __isl_take isl_dim *set_dim);
847 __isl_give isl_map *isl_map_lex_le(
848 __isl_take isl_dim *set_dim);
849 __isl_give isl_map *isl_map_lex_gt(
850 __isl_take isl_dim *set_dim);
851 __isl_give isl_map *isl_map_lex_ge(
852 __isl_take isl_dim *set_dim);
853 __isl_give isl_map *isl_map_lex_lt_first(
854 __isl_take isl_dim *dim, unsigned n);
855 __isl_give isl_map *isl_map_lex_le_first(
856 __isl_take isl_dim *dim, unsigned n);
857 __isl_give isl_map *isl_map_lex_gt_first(
858 __isl_take isl_dim *dim, unsigned n);
859 __isl_give isl_map *isl_map_lex_ge_first(
860 __isl_take isl_dim *dim, unsigned n);
862 The first four functions take a dimension specification for a B<set>
863 and return relations that express that the elements in the domain
864 are lexicographically less
865 (C<isl_map_lex_lt>), less or equal (C<isl_map_lex_le>),
866 greater (C<isl_map_lex_gt>) or greater or equal (C<isl_map_lex_ge>)
867 than the elements in the range.
868 The last four functions take a dimension specification for a map
869 and return relations that express that the first C<n> dimensions
870 in the domain are lexicographically less
871 (C<isl_map_lex_lt_first>), less or equal (C<isl_map_lex_le_first>),
872 greater (C<isl_map_lex_gt_first>) or greater or equal (C<isl_map_lex_ge_first>)
873 than the first C<n> dimensions in the range.
877 A basic set or relation can be converted to a set or relation
878 using the following functions.
880 __isl_give isl_set *isl_set_from_basic_set(
881 __isl_take isl_basic_set *bset);
882 __isl_give isl_map *isl_map_from_basic_map(
883 __isl_take isl_basic_map *bmap);
885 Sets and relations can be converted to union sets and relations
886 using the following functions.
888 __isl_give isl_union_map *isl_union_map_from_map(
889 __isl_take isl_map *map);
890 __isl_give isl_union_set *isl_union_set_from_set(
891 __isl_take isl_set *set);
893 Sets and relations can be copied and freed again using the following
896 __isl_give isl_basic_set *isl_basic_set_copy(
897 __isl_keep isl_basic_set *bset);
898 __isl_give isl_set *isl_set_copy(__isl_keep isl_set *set);
899 __isl_give isl_union_set *isl_union_set_copy(
900 __isl_keep isl_union_set *uset);
901 __isl_give isl_basic_map *isl_basic_map_copy(
902 __isl_keep isl_basic_map *bmap);
903 __isl_give isl_map *isl_map_copy(__isl_keep isl_map *map);
904 __isl_give isl_union_map *isl_union_map_copy(
905 __isl_keep isl_union_map *umap);
906 void isl_basic_set_free(__isl_take isl_basic_set *bset);
907 void isl_set_free(__isl_take isl_set *set);
908 void isl_union_set_free(__isl_take isl_union_set *uset);
909 void isl_basic_map_free(__isl_take isl_basic_map *bmap);
910 void isl_map_free(__isl_take isl_map *map);
911 void isl_union_map_free(__isl_take isl_union_map *umap);
913 Other sets and relations can be constructed by starting
914 from a universe set or relation, adding equality and/or
915 inequality constraints and then projecting out the
916 existentially quantified variables, if any.
917 Constraints can be constructed, manipulated and
918 added to (basic) sets and relations using the following functions.
920 #include <isl/constraint.h>
921 __isl_give isl_constraint *isl_equality_alloc(
922 __isl_take isl_dim *dim);
923 __isl_give isl_constraint *isl_inequality_alloc(
924 __isl_take isl_dim *dim);
925 void isl_constraint_set_constant(
926 __isl_keep isl_constraint *constraint, isl_int v);
927 void isl_constraint_set_coefficient(
928 __isl_keep isl_constraint *constraint,
929 enum isl_dim_type type, int pos, isl_int v);
930 __isl_give isl_basic_map *isl_basic_map_add_constraint(
931 __isl_take isl_basic_map *bmap,
932 __isl_take isl_constraint *constraint);
933 __isl_give isl_basic_set *isl_basic_set_add_constraint(
934 __isl_take isl_basic_set *bset,
935 __isl_take isl_constraint *constraint);
936 __isl_give isl_map *isl_map_add_constraint(
937 __isl_take isl_map *map,
938 __isl_take isl_constraint *constraint);
939 __isl_give isl_set *isl_set_add_constraint(
940 __isl_take isl_set *set,
941 __isl_take isl_constraint *constraint);
943 For example, to create a set containing the even integers
944 between 10 and 42, you would use the following code.
948 struct isl_constraint *c;
949 struct isl_basic_set *bset;
952 dim = isl_dim_set_alloc(ctx, 0, 2);
953 bset = isl_basic_set_universe(isl_dim_copy(dim));
955 c = isl_equality_alloc(isl_dim_copy(dim));
956 isl_int_set_si(v, -1);
957 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
958 isl_int_set_si(v, 2);
959 isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
960 bset = isl_basic_set_add_constraint(bset, c);
962 c = isl_inequality_alloc(isl_dim_copy(dim));
963 isl_int_set_si(v, -10);
964 isl_constraint_set_constant(c, v);
965 isl_int_set_si(v, 1);
966 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
967 bset = isl_basic_set_add_constraint(bset, c);
969 c = isl_inequality_alloc(dim);
970 isl_int_set_si(v, 42);
971 isl_constraint_set_constant(c, v);
972 isl_int_set_si(v, -1);
973 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
974 bset = isl_basic_set_add_constraint(bset, c);
976 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
982 struct isl_basic_set *bset;
983 bset = isl_basic_set_read_from_str(ctx,
984 "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}", -1);
986 A basic set or relation can also be constructed from two matrices
987 describing the equalities and the inequalities.
989 __isl_give isl_basic_set *isl_basic_set_from_constraint_matrices(
990 __isl_take isl_dim *dim,
991 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
992 enum isl_dim_type c1,
993 enum isl_dim_type c2, enum isl_dim_type c3,
994 enum isl_dim_type c4);
995 __isl_give isl_basic_map *isl_basic_map_from_constraint_matrices(
996 __isl_take isl_dim *dim,
997 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
998 enum isl_dim_type c1,
999 enum isl_dim_type c2, enum isl_dim_type c3,
1000 enum isl_dim_type c4, enum isl_dim_type c5);
1002 The C<isl_dim_type> arguments indicate the order in which
1003 different kinds of variables appear in the input matrices
1004 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1005 C<isl_dim_set> and C<isl_dim_div> for sets and
1006 of C<isl_dim_cst>, C<isl_dim_param>,
1007 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div> for relations.
1009 =head2 Inspecting Sets and Relations
1011 Usually, the user should not have to care about the actual constraints
1012 of the sets and maps, but should instead apply the abstract operations
1013 explained in the following sections.
1014 Occasionally, however, it may be required to inspect the individual
1015 coefficients of the constraints. This section explains how to do so.
1016 In these cases, it may also be useful to have C<isl> compute
1017 an explicit representation of the existentially quantified variables.
1019 __isl_give isl_set *isl_set_compute_divs(
1020 __isl_take isl_set *set);
1021 __isl_give isl_map *isl_map_compute_divs(
1022 __isl_take isl_map *map);
1023 __isl_give isl_union_set *isl_union_set_compute_divs(
1024 __isl_take isl_union_set *uset);
1025 __isl_give isl_union_map *isl_union_map_compute_divs(
1026 __isl_take isl_union_map *umap);
1028 This explicit representation defines the existentially quantified
1029 variables as integer divisions of the other variables, possibly
1030 including earlier existentially quantified variables.
1031 An explicitly represented existentially quantified variable therefore
1032 has a unique value when the values of the other variables are known.
1033 If, furthermore, the same existentials, i.e., existentials
1034 with the same explicit representations, should appear in the
1035 same order in each of the disjuncts of a set or map, then the user should call
1036 either of the following functions.
1038 __isl_give isl_set *isl_set_align_divs(
1039 __isl_take isl_set *set);
1040 __isl_give isl_map *isl_map_align_divs(
1041 __isl_take isl_map *map);
1043 Alternatively, the existentially quantified variables can be removed
1044 using the following functions, which compute an overapproximation.
1046 __isl_give isl_basic_set *isl_basic_set_remove_divs(
1047 __isl_take isl_basic_set *bset);
1048 __isl_give isl_basic_map *isl_basic_map_remove_divs(
1049 __isl_take isl_basic_map *bmap);
1050 __isl_give isl_set *isl_set_remove_divs(
1051 __isl_take isl_set *set);
1052 __isl_give isl_map *isl_map_remove_divs(
1053 __isl_take isl_map *map);
1055 To iterate over all the sets or maps in a union set or map, use
1057 int isl_union_set_foreach_set(__isl_keep isl_union_set *uset,
1058 int (*fn)(__isl_take isl_set *set, void *user),
1060 int isl_union_map_foreach_map(__isl_keep isl_union_map *umap,
1061 int (*fn)(__isl_take isl_map *map, void *user),
1064 The number of sets or maps in a union set or map can be obtained
1067 int isl_union_set_n_set(__isl_keep isl_union_set *uset);
1068 int isl_union_map_n_map(__isl_keep isl_union_map *umap);
1070 To extract the set or map from a union with a given dimension
1073 __isl_give isl_set *isl_union_set_extract_set(
1074 __isl_keep isl_union_set *uset,
1075 __isl_take isl_dim *dim);
1076 __isl_give isl_map *isl_union_map_extract_map(
1077 __isl_keep isl_union_map *umap,
1078 __isl_take isl_dim *dim);
1080 To iterate over all the basic sets or maps in a set or map, use
1082 int isl_set_foreach_basic_set(__isl_keep isl_set *set,
1083 int (*fn)(__isl_take isl_basic_set *bset, void *user),
1085 int isl_map_foreach_basic_map(__isl_keep isl_map *map,
1086 int (*fn)(__isl_take isl_basic_map *bmap, void *user),
1089 The callback function C<fn> should return 0 if successful and
1090 -1 if an error occurs. In the latter case, or if any other error
1091 occurs, the above functions will return -1.
1093 It should be noted that C<isl> does not guarantee that
1094 the basic sets or maps passed to C<fn> are disjoint.
1095 If this is required, then the user should call one of
1096 the following functions first.
1098 __isl_give isl_set *isl_set_make_disjoint(
1099 __isl_take isl_set *set);
1100 __isl_give isl_map *isl_map_make_disjoint(
1101 __isl_take isl_map *map);
1103 The number of basic sets in a set can be obtained
1106 int isl_set_n_basic_set(__isl_keep isl_set *set);
1108 To iterate over the constraints of a basic set or map, use
1110 #include <isl/constraint.h>
1112 int isl_basic_map_foreach_constraint(
1113 __isl_keep isl_basic_map *bmap,
1114 int (*fn)(__isl_take isl_constraint *c, void *user),
1116 void isl_constraint_free(struct isl_constraint *c);
1118 Again, the callback function C<fn> should return 0 if successful and
1119 -1 if an error occurs. In the latter case, or if any other error
1120 occurs, the above functions will return -1.
1121 The constraint C<c> represents either an equality or an inequality.
1122 Use the following function to find out whether a constraint
1123 represents an equality. If not, it represents an inequality.
1125 int isl_constraint_is_equality(
1126 __isl_keep isl_constraint *constraint);
1128 The coefficients of the constraints can be inspected using
1129 the following functions.
1131 void isl_constraint_get_constant(
1132 __isl_keep isl_constraint *constraint, isl_int *v);
1133 void isl_constraint_get_coefficient(
1134 __isl_keep isl_constraint *constraint,
1135 enum isl_dim_type type, int pos, isl_int *v);
1136 int isl_constraint_involves_dims(
1137 __isl_keep isl_constraint *constraint,
1138 enum isl_dim_type type, unsigned first, unsigned n);
1140 The explicit representations of the existentially quantified
1141 variables can be inspected using the following functions.
1142 Note that the user is only allowed to use these functions
1143 if the inspected set or map is the result of a call
1144 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
1146 __isl_give isl_div *isl_constraint_div(
1147 __isl_keep isl_constraint *constraint, int pos);
1148 isl_ctx *isl_div_get_ctx(__isl_keep isl_div *div);
1149 void isl_div_get_constant(__isl_keep isl_div *div,
1151 void isl_div_get_denominator(__isl_keep isl_div *div,
1153 void isl_div_get_coefficient(__isl_keep isl_div *div,
1154 enum isl_dim_type type, int pos, isl_int *v);
1156 To obtain the constraints of a basic set or map in matrix
1157 form, use the following functions.
1159 __isl_give isl_mat *isl_basic_set_equalities_matrix(
1160 __isl_keep isl_basic_set *bset,
1161 enum isl_dim_type c1, enum isl_dim_type c2,
1162 enum isl_dim_type c3, enum isl_dim_type c4);
1163 __isl_give isl_mat *isl_basic_set_inequalities_matrix(
1164 __isl_keep isl_basic_set *bset,
1165 enum isl_dim_type c1, enum isl_dim_type c2,
1166 enum isl_dim_type c3, enum isl_dim_type c4);
1167 __isl_give isl_mat *isl_basic_map_equalities_matrix(
1168 __isl_keep isl_basic_map *bmap,
1169 enum isl_dim_type c1,
1170 enum isl_dim_type c2, enum isl_dim_type c3,
1171 enum isl_dim_type c4, enum isl_dim_type c5);
1172 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
1173 __isl_keep isl_basic_map *bmap,
1174 enum isl_dim_type c1,
1175 enum isl_dim_type c2, enum isl_dim_type c3,
1176 enum isl_dim_type c4, enum isl_dim_type c5);
1178 The C<isl_dim_type> arguments dictate the order in which
1179 different kinds of variables appear in the resulting matrix
1180 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1181 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
1183 The names of the domain and range spaces of a set or relation can be
1184 read off using the following functions.
1186 const char *isl_basic_set_get_tuple_name(
1187 __isl_keep isl_basic_set *bset);
1188 const char *isl_set_get_tuple_name(
1189 __isl_keep isl_set *set);
1190 const char *isl_basic_map_get_tuple_name(
1191 __isl_keep isl_basic_map *bmap,
1192 enum isl_dim_type type);
1193 const char *isl_map_get_tuple_name(
1194 __isl_keep isl_map *map,
1195 enum isl_dim_type type);
1197 As with C<isl_dim_get_tuple_name>, the value returned points to
1198 an internal data structure.
1199 The names of individual dimensions can be read off using
1200 the following functions.
1202 const char *isl_constraint_get_dim_name(
1203 __isl_keep isl_constraint *constraint,
1204 enum isl_dim_type type, unsigned pos);
1205 const char *isl_basic_set_get_dim_name(
1206 __isl_keep isl_basic_set *bset,
1207 enum isl_dim_type type, unsigned pos);
1208 const char *isl_set_get_dim_name(
1209 __isl_keep isl_set *set,
1210 enum isl_dim_type type, unsigned pos);
1211 const char *isl_basic_map_get_dim_name(
1212 __isl_keep isl_basic_map *bmap,
1213 enum isl_dim_type type, unsigned pos);
1214 const char *isl_map_get_dim_name(
1215 __isl_keep isl_map *map,
1216 enum isl_dim_type type, unsigned pos);
1218 These functions are mostly useful to obtain the names
1223 =head3 Unary Properties
1229 The following functions test whether the given set or relation
1230 contains any integer points. The ``plain'' variants do not perform
1231 any computations, but simply check if the given set or relation
1232 is already known to be empty.
1234 int isl_basic_set_plain_is_empty(__isl_keep isl_basic_set *bset);
1235 int isl_basic_set_is_empty(__isl_keep isl_basic_set *bset);
1236 int isl_set_plain_is_empty(__isl_keep isl_set *set);
1237 int isl_set_is_empty(__isl_keep isl_set *set);
1238 int isl_union_set_is_empty(__isl_keep isl_union_set *uset);
1239 int isl_basic_map_plain_is_empty(__isl_keep isl_basic_map *bmap);
1240 int isl_basic_map_is_empty(__isl_keep isl_basic_map *bmap);
1241 int isl_map_plain_is_empty(__isl_keep isl_map *map);
1242 int isl_map_is_empty(__isl_keep isl_map *map);
1243 int isl_union_map_is_empty(__isl_keep isl_union_map *umap);
1245 =item * Universality
1247 int isl_basic_set_is_universe(__isl_keep isl_basic_set *bset);
1248 int isl_basic_map_is_universe(__isl_keep isl_basic_map *bmap);
1249 int isl_set_plain_is_universe(__isl_keep isl_set *set);
1251 =item * Single-valuedness
1253 int isl_map_is_single_valued(__isl_keep isl_map *map);
1254 int isl_union_map_is_single_valued(__isl_keep isl_union_map *umap);
1258 int isl_map_plain_is_injective(__isl_keep isl_map *map);
1259 int isl_map_is_injective(__isl_keep isl_map *map);
1260 int isl_union_map_plain_is_injective(
1261 __isl_keep isl_union_map *umap);
1262 int isl_union_map_is_injective(
1263 __isl_keep isl_union_map *umap);
1267 int isl_map_is_bijective(__isl_keep isl_map *map);
1268 int isl_union_map_is_bijective(__isl_keep isl_union_map *umap);
1272 The following functions check whether the domain of the given
1273 (basic) set is a wrapped relation.
1275 int isl_basic_set_is_wrapping(
1276 __isl_keep isl_basic_set *bset);
1277 int isl_set_is_wrapping(__isl_keep isl_set *set);
1279 =item * Internal Product
1281 int isl_basic_map_can_zip(
1282 __isl_keep isl_basic_map *bmap);
1283 int isl_map_can_zip(__isl_keep isl_map *map);
1285 Check whether the product of domain and range of the given relation
1287 i.e., whether both domain and range are nested relations.
1291 =head3 Binary Properties
1297 int isl_set_plain_is_equal(__isl_keep isl_set *set1,
1298 __isl_keep isl_set *set2);
1299 int isl_set_is_equal(__isl_keep isl_set *set1,
1300 __isl_keep isl_set *set2);
1301 int isl_union_set_is_equal(
1302 __isl_keep isl_union_set *uset1,
1303 __isl_keep isl_union_set *uset2);
1304 int isl_basic_map_is_equal(
1305 __isl_keep isl_basic_map *bmap1,
1306 __isl_keep isl_basic_map *bmap2);
1307 int isl_map_is_equal(__isl_keep isl_map *map1,
1308 __isl_keep isl_map *map2);
1309 int isl_map_plain_is_equal(__isl_keep isl_map *map1,
1310 __isl_keep isl_map *map2);
1311 int isl_union_map_is_equal(
1312 __isl_keep isl_union_map *umap1,
1313 __isl_keep isl_union_map *umap2);
1315 =item * Disjointness
1317 int isl_set_plain_is_disjoint(__isl_keep isl_set *set1,
1318 __isl_keep isl_set *set2);
1322 int isl_set_is_subset(__isl_keep isl_set *set1,
1323 __isl_keep isl_set *set2);
1324 int isl_set_is_strict_subset(
1325 __isl_keep isl_set *set1,
1326 __isl_keep isl_set *set2);
1327 int isl_union_set_is_subset(
1328 __isl_keep isl_union_set *uset1,
1329 __isl_keep isl_union_set *uset2);
1330 int isl_union_set_is_strict_subset(
1331 __isl_keep isl_union_set *uset1,
1332 __isl_keep isl_union_set *uset2);
1333 int isl_basic_map_is_subset(
1334 __isl_keep isl_basic_map *bmap1,
1335 __isl_keep isl_basic_map *bmap2);
1336 int isl_basic_map_is_strict_subset(
1337 __isl_keep isl_basic_map *bmap1,
1338 __isl_keep isl_basic_map *bmap2);
1339 int isl_map_is_subset(
1340 __isl_keep isl_map *map1,
1341 __isl_keep isl_map *map2);
1342 int isl_map_is_strict_subset(
1343 __isl_keep isl_map *map1,
1344 __isl_keep isl_map *map2);
1345 int isl_union_map_is_subset(
1346 __isl_keep isl_union_map *umap1,
1347 __isl_keep isl_union_map *umap2);
1348 int isl_union_map_is_strict_subset(
1349 __isl_keep isl_union_map *umap1,
1350 __isl_keep isl_union_map *umap2);
1354 =head2 Unary Operations
1360 __isl_give isl_set *isl_set_complement(
1361 __isl_take isl_set *set);
1365 __isl_give isl_basic_map *isl_basic_map_reverse(
1366 __isl_take isl_basic_map *bmap);
1367 __isl_give isl_map *isl_map_reverse(
1368 __isl_take isl_map *map);
1369 __isl_give isl_union_map *isl_union_map_reverse(
1370 __isl_take isl_union_map *umap);
1374 __isl_give isl_basic_set *isl_basic_set_project_out(
1375 __isl_take isl_basic_set *bset,
1376 enum isl_dim_type type, unsigned first, unsigned n);
1377 __isl_give isl_basic_map *isl_basic_map_project_out(
1378 __isl_take isl_basic_map *bmap,
1379 enum isl_dim_type type, unsigned first, unsigned n);
1380 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
1381 enum isl_dim_type type, unsigned first, unsigned n);
1382 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
1383 enum isl_dim_type type, unsigned first, unsigned n);
1384 __isl_give isl_basic_set *isl_basic_map_domain(
1385 __isl_take isl_basic_map *bmap);
1386 __isl_give isl_basic_set *isl_basic_map_range(
1387 __isl_take isl_basic_map *bmap);
1388 __isl_give isl_set *isl_map_domain(
1389 __isl_take isl_map *bmap);
1390 __isl_give isl_set *isl_map_range(
1391 __isl_take isl_map *map);
1392 __isl_give isl_union_set *isl_union_map_domain(
1393 __isl_take isl_union_map *umap);
1394 __isl_give isl_union_set *isl_union_map_range(
1395 __isl_take isl_union_map *umap);
1397 __isl_give isl_basic_map *isl_basic_map_domain_map(
1398 __isl_take isl_basic_map *bmap);
1399 __isl_give isl_basic_map *isl_basic_map_range_map(
1400 __isl_take isl_basic_map *bmap);
1401 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
1402 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
1403 __isl_give isl_union_map *isl_union_map_domain_map(
1404 __isl_take isl_union_map *umap);
1405 __isl_give isl_union_map *isl_union_map_range_map(
1406 __isl_take isl_union_map *umap);
1408 The functions above construct a (basic, regular or union) relation
1409 that maps (a wrapped version of) the input relation to its domain or range.
1413 __isl_give isl_set *isl_set_eliminate(
1414 __isl_take isl_set *set, enum isl_dim_type type,
1415 unsigned first, unsigned n);
1417 Eliminate the coefficients for the given dimensions from the constraints,
1418 without removing the dimensions.
1422 __isl_give isl_map *isl_set_identity(
1423 __isl_take isl_set *set);
1424 __isl_give isl_union_map *isl_union_set_identity(
1425 __isl_take isl_union_set *uset);
1427 Construct an identity relation on the given (union) set.
1431 __isl_give isl_basic_set *isl_basic_map_deltas(
1432 __isl_take isl_basic_map *bmap);
1433 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
1434 __isl_give isl_union_set *isl_union_map_deltas(
1435 __isl_take isl_union_map *umap);
1437 These functions return a (basic) set containing the differences
1438 between image elements and corresponding domain elements in the input.
1440 __isl_give isl_basic_map *isl_basic_map_deltas_map(
1441 __isl_take isl_basic_map *bmap);
1442 __isl_give isl_map *isl_map_deltas_map(
1443 __isl_take isl_map *map);
1444 __isl_give isl_union_map *isl_union_map_deltas_map(
1445 __isl_take isl_union_map *umap);
1447 The functions above construct a (basic, regular or union) relation
1448 that maps (a wrapped version of) the input relation to its delta set.
1452 Simplify the representation of a set or relation by trying
1453 to combine pairs of basic sets or relations into a single
1454 basic set or relation.
1456 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
1457 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
1458 __isl_give isl_union_set *isl_union_set_coalesce(
1459 __isl_take isl_union_set *uset);
1460 __isl_give isl_union_map *isl_union_map_coalesce(
1461 __isl_take isl_union_map *umap);
1463 =item * Detecting equalities
1465 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
1466 __isl_take isl_basic_set *bset);
1467 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
1468 __isl_take isl_basic_map *bmap);
1469 __isl_give isl_set *isl_set_detect_equalities(
1470 __isl_take isl_set *set);
1471 __isl_give isl_map *isl_map_detect_equalities(
1472 __isl_take isl_map *map);
1473 __isl_give isl_union_set *isl_union_set_detect_equalities(
1474 __isl_take isl_union_set *uset);
1475 __isl_give isl_union_map *isl_union_map_detect_equalities(
1476 __isl_take isl_union_map *umap);
1478 Simplify the representation of a set or relation by detecting implicit
1481 =item * Removing redundant constraints
1483 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
1484 __isl_take isl_basic_set *bset);
1485 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
1486 __isl_take isl_basic_map *bmap);
1490 __isl_give isl_basic_set *isl_set_convex_hull(
1491 __isl_take isl_set *set);
1492 __isl_give isl_basic_map *isl_map_convex_hull(
1493 __isl_take isl_map *map);
1495 If the input set or relation has any existentially quantified
1496 variables, then the result of these operations is currently undefined.
1500 __isl_give isl_basic_set *isl_set_simple_hull(
1501 __isl_take isl_set *set);
1502 __isl_give isl_basic_map *isl_map_simple_hull(
1503 __isl_take isl_map *map);
1504 __isl_give isl_union_map *isl_union_map_simple_hull(
1505 __isl_take isl_union_map *umap);
1507 These functions compute a single basic set or relation
1508 that contains the whole input set or relation.
1509 In particular, the output is described by translates
1510 of the constraints describing the basic sets or relations in the input.
1514 (See \autoref{s:simple hull}.)
1520 __isl_give isl_basic_set *isl_basic_set_affine_hull(
1521 __isl_take isl_basic_set *bset);
1522 __isl_give isl_basic_set *isl_set_affine_hull(
1523 __isl_take isl_set *set);
1524 __isl_give isl_union_set *isl_union_set_affine_hull(
1525 __isl_take isl_union_set *uset);
1526 __isl_give isl_basic_map *isl_basic_map_affine_hull(
1527 __isl_take isl_basic_map *bmap);
1528 __isl_give isl_basic_map *isl_map_affine_hull(
1529 __isl_take isl_map *map);
1530 __isl_give isl_union_map *isl_union_map_affine_hull(
1531 __isl_take isl_union_map *umap);
1533 In case of union sets and relations, the affine hull is computed
1536 =item * Polyhedral hull
1538 __isl_give isl_basic_set *isl_set_polyhedral_hull(
1539 __isl_take isl_set *set);
1540 __isl_give isl_basic_map *isl_map_polyhedral_hull(
1541 __isl_take isl_map *map);
1542 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
1543 __isl_take isl_union_set *uset);
1544 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
1545 __isl_take isl_union_map *umap);
1547 These functions compute a single basic set or relation
1548 not involving any existentially quantified variables
1549 that contains the whole input set or relation.
1550 In case of union sets and relations, the polyhedral hull is computed
1553 =item * Optimization
1555 #include <isl/ilp.h>
1556 enum isl_lp_result isl_basic_set_max(
1557 __isl_keep isl_basic_set *bset,
1558 __isl_keep isl_aff *obj, isl_int *opt)
1559 enum isl_lp_result isl_set_max(__isl_keep isl_set *set,
1560 __isl_keep isl_aff *obj, isl_int *opt);
1562 Compute the maximum of the integer affine expression C<obj>
1563 over the points in C<set>, returning the result in C<opt>.
1564 The return value may be one of C<isl_lp_error>,
1565 C<isl_lp_ok>, C<isl_lp_unbounded> or C<isl_lp_empty>.
1569 The following functions compute either the set of (rational) coefficient
1570 values of valid constraints for the given set or the set of (rational)
1571 values satisfying the constraints with coefficients from the given set.
1572 Internally, these two sets of functions perform essentially the
1573 same operations, except that the set of coefficients is assumed to
1574 be a cone, while the set of values may be any polyhedron.
1575 The current implementation is based on the Farkas lemma and
1576 Fourier-Motzkin elimination, but this may change or be made optional
1577 in future. In particular, future implementations may use different
1578 dualization algorithms or skip the elimination step.
1580 __isl_give isl_basic_set *isl_basic_set_coefficients(
1581 __isl_take isl_basic_set *bset);
1582 __isl_give isl_basic_set *isl_set_coefficients(
1583 __isl_take isl_set *set);
1584 __isl_give isl_union_set *isl_union_set_coefficients(
1585 __isl_take isl_union_set *bset);
1586 __isl_give isl_basic_set *isl_basic_set_solutions(
1587 __isl_take isl_basic_set *bset);
1588 __isl_give isl_basic_set *isl_set_solutions(
1589 __isl_take isl_set *set);
1590 __isl_give isl_union_set *isl_union_set_solutions(
1591 __isl_take isl_union_set *bset);
1595 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
1597 __isl_give isl_union_map *isl_union_map_power(
1598 __isl_take isl_union_map *umap, int *exact);
1600 Compute a parametric representation for all positive powers I<k> of C<map>.
1601 The result maps I<k> to a nested relation corresponding to the
1602 I<k>th power of C<map>.
1603 The result may be an overapproximation. If the result is known to be exact,
1604 then C<*exact> is set to C<1>.
1606 =item * Transitive closure
1608 __isl_give isl_map *isl_map_transitive_closure(
1609 __isl_take isl_map *map, int *exact);
1610 __isl_give isl_union_map *isl_union_map_transitive_closure(
1611 __isl_take isl_union_map *umap, int *exact);
1613 Compute the transitive closure of C<map>.
1614 The result may be an overapproximation. If the result is known to be exact,
1615 then C<*exact> is set to C<1>.
1617 =item * Reaching path lengths
1619 __isl_give isl_map *isl_map_reaching_path_lengths(
1620 __isl_take isl_map *map, int *exact);
1622 Compute a relation that maps each element in the range of C<map>
1623 to the lengths of all paths composed of edges in C<map> that
1624 end up in the given element.
1625 The result may be an overapproximation. If the result is known to be exact,
1626 then C<*exact> is set to C<1>.
1627 To compute the I<maximal> path length, the resulting relation
1628 should be postprocessed by C<isl_map_lexmax>.
1629 In particular, if the input relation is a dependence relation
1630 (mapping sources to sinks), then the maximal path length corresponds
1631 to the free schedule.
1632 Note, however, that C<isl_map_lexmax> expects the maximum to be
1633 finite, so if the path lengths are unbounded (possibly due to
1634 the overapproximation), then you will get an error message.
1638 __isl_give isl_basic_set *isl_basic_map_wrap(
1639 __isl_take isl_basic_map *bmap);
1640 __isl_give isl_set *isl_map_wrap(
1641 __isl_take isl_map *map);
1642 __isl_give isl_union_set *isl_union_map_wrap(
1643 __isl_take isl_union_map *umap);
1644 __isl_give isl_basic_map *isl_basic_set_unwrap(
1645 __isl_take isl_basic_set *bset);
1646 __isl_give isl_map *isl_set_unwrap(
1647 __isl_take isl_set *set);
1648 __isl_give isl_union_map *isl_union_set_unwrap(
1649 __isl_take isl_union_set *uset);
1653 Remove any internal structure of domain (and range) of the given
1654 set or relation. If there is any such internal structure in the input,
1655 then the name of the space is also removed.
1657 __isl_give isl_basic_set *isl_basic_set_flatten(
1658 __isl_take isl_basic_set *bset);
1659 __isl_give isl_set *isl_set_flatten(
1660 __isl_take isl_set *set);
1661 __isl_give isl_basic_map *isl_basic_map_flatten(
1662 __isl_take isl_basic_map *bmap);
1663 __isl_give isl_map *isl_map_flatten(
1664 __isl_take isl_map *map);
1666 __isl_give isl_map *isl_set_flatten_map(
1667 __isl_take isl_set *set);
1669 The function above constructs a relation
1670 that maps the input set to a flattened version of the set.
1674 Lift the input set to a space with extra dimensions corresponding
1675 to the existentially quantified variables in the input.
1676 In particular, the result lives in a wrapped map where the domain
1677 is the original space and the range corresponds to the original
1678 existentially quantified variables.
1680 __isl_give isl_basic_set *isl_basic_set_lift(
1681 __isl_take isl_basic_set *bset);
1682 __isl_give isl_set *isl_set_lift(
1683 __isl_take isl_set *set);
1684 __isl_give isl_union_set *isl_union_set_lift(
1685 __isl_take isl_union_set *uset);
1687 =item * Internal Product
1689 __isl_give isl_basic_map *isl_basic_map_zip(
1690 __isl_take isl_basic_map *bmap);
1691 __isl_give isl_map *isl_map_zip(
1692 __isl_take isl_map *map);
1693 __isl_give isl_union_map *isl_union_map_zip(
1694 __isl_take isl_union_map *umap);
1696 Given a relation with nested relations for domain and range,
1697 interchange the range of the domain with the domain of the range.
1699 =item * Aligning parameters
1701 __isl_give isl_set *isl_set_align_params(
1702 __isl_take isl_set *set,
1703 __isl_take isl_dim *model);
1704 __isl_give isl_map *isl_map_align_params(
1705 __isl_take isl_map *map,
1706 __isl_take isl_dim *model);
1708 Change the order of the parameters of the given set or relation
1709 such that the first parameters match those of C<model>.
1710 This may involve the introduction of extra parameters.
1711 All parameters need to be named.
1713 =item * Dimension manipulation
1715 __isl_give isl_set *isl_set_add_dims(
1716 __isl_take isl_set *set,
1717 enum isl_dim_type type, unsigned n);
1718 __isl_give isl_map *isl_map_add_dims(
1719 __isl_take isl_map *map,
1720 enum isl_dim_type type, unsigned n);
1722 It is usually not advisable to directly change the (input or output)
1723 space of a set or a relation as this removes the name and the internal
1724 structure of the space. However, the above functions can be useful
1725 to add new parameters, assuming
1726 C<isl_set_align_params> and C<isl_map_align_params>
1731 =head2 Binary Operations
1733 The two arguments of a binary operation not only need to live
1734 in the same C<isl_ctx>, they currently also need to have
1735 the same (number of) parameters.
1737 =head3 Basic Operations
1741 =item * Intersection
1743 __isl_give isl_basic_set *isl_basic_set_intersect(
1744 __isl_take isl_basic_set *bset1,
1745 __isl_take isl_basic_set *bset2);
1746 __isl_give isl_set *isl_set_intersect(
1747 __isl_take isl_set *set1,
1748 __isl_take isl_set *set2);
1749 __isl_give isl_union_set *isl_union_set_intersect(
1750 __isl_take isl_union_set *uset1,
1751 __isl_take isl_union_set *uset2);
1752 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
1753 __isl_take isl_basic_map *bmap,
1754 __isl_take isl_basic_set *bset);
1755 __isl_give isl_basic_map *isl_basic_map_intersect_range(
1756 __isl_take isl_basic_map *bmap,
1757 __isl_take isl_basic_set *bset);
1758 __isl_give isl_basic_map *isl_basic_map_intersect(
1759 __isl_take isl_basic_map *bmap1,
1760 __isl_take isl_basic_map *bmap2);
1761 __isl_give isl_map *isl_map_intersect_domain(
1762 __isl_take isl_map *map,
1763 __isl_take isl_set *set);
1764 __isl_give isl_map *isl_map_intersect_range(
1765 __isl_take isl_map *map,
1766 __isl_take isl_set *set);
1767 __isl_give isl_map *isl_map_intersect(
1768 __isl_take isl_map *map1,
1769 __isl_take isl_map *map2);
1770 __isl_give isl_union_map *isl_union_map_intersect_domain(
1771 __isl_take isl_union_map *umap,
1772 __isl_take isl_union_set *uset);
1773 __isl_give isl_union_map *isl_union_map_intersect_range(
1774 __isl_take isl_union_map *umap,
1775 __isl_take isl_union_set *uset);
1776 __isl_give isl_union_map *isl_union_map_intersect(
1777 __isl_take isl_union_map *umap1,
1778 __isl_take isl_union_map *umap2);
1782 __isl_give isl_set *isl_basic_set_union(
1783 __isl_take isl_basic_set *bset1,
1784 __isl_take isl_basic_set *bset2);
1785 __isl_give isl_map *isl_basic_map_union(
1786 __isl_take isl_basic_map *bmap1,
1787 __isl_take isl_basic_map *bmap2);
1788 __isl_give isl_set *isl_set_union(
1789 __isl_take isl_set *set1,
1790 __isl_take isl_set *set2);
1791 __isl_give isl_map *isl_map_union(
1792 __isl_take isl_map *map1,
1793 __isl_take isl_map *map2);
1794 __isl_give isl_union_set *isl_union_set_union(
1795 __isl_take isl_union_set *uset1,
1796 __isl_take isl_union_set *uset2);
1797 __isl_give isl_union_map *isl_union_map_union(
1798 __isl_take isl_union_map *umap1,
1799 __isl_take isl_union_map *umap2);
1801 =item * Set difference
1803 __isl_give isl_set *isl_set_subtract(
1804 __isl_take isl_set *set1,
1805 __isl_take isl_set *set2);
1806 __isl_give isl_map *isl_map_subtract(
1807 __isl_take isl_map *map1,
1808 __isl_take isl_map *map2);
1809 __isl_give isl_union_set *isl_union_set_subtract(
1810 __isl_take isl_union_set *uset1,
1811 __isl_take isl_union_set *uset2);
1812 __isl_give isl_union_map *isl_union_map_subtract(
1813 __isl_take isl_union_map *umap1,
1814 __isl_take isl_union_map *umap2);
1818 __isl_give isl_basic_set *isl_basic_set_apply(
1819 __isl_take isl_basic_set *bset,
1820 __isl_take isl_basic_map *bmap);
1821 __isl_give isl_set *isl_set_apply(
1822 __isl_take isl_set *set,
1823 __isl_take isl_map *map);
1824 __isl_give isl_union_set *isl_union_set_apply(
1825 __isl_take isl_union_set *uset,
1826 __isl_take isl_union_map *umap);
1827 __isl_give isl_basic_map *isl_basic_map_apply_domain(
1828 __isl_take isl_basic_map *bmap1,
1829 __isl_take isl_basic_map *bmap2);
1830 __isl_give isl_basic_map *isl_basic_map_apply_range(
1831 __isl_take isl_basic_map *bmap1,
1832 __isl_take isl_basic_map *bmap2);
1833 __isl_give isl_map *isl_map_apply_domain(
1834 __isl_take isl_map *map1,
1835 __isl_take isl_map *map2);
1836 __isl_give isl_union_map *isl_union_map_apply_domain(
1837 __isl_take isl_union_map *umap1,
1838 __isl_take isl_union_map *umap2);
1839 __isl_give isl_map *isl_map_apply_range(
1840 __isl_take isl_map *map1,
1841 __isl_take isl_map *map2);
1842 __isl_give isl_union_map *isl_union_map_apply_range(
1843 __isl_take isl_union_map *umap1,
1844 __isl_take isl_union_map *umap2);
1846 =item * Cartesian Product
1848 __isl_give isl_set *isl_set_product(
1849 __isl_take isl_set *set1,
1850 __isl_take isl_set *set2);
1851 __isl_give isl_union_set *isl_union_set_product(
1852 __isl_take isl_union_set *uset1,
1853 __isl_take isl_union_set *uset2);
1854 __isl_give isl_basic_map *isl_basic_map_range_product(
1855 __isl_take isl_basic_map *bmap1,
1856 __isl_take isl_basic_map *bmap2);
1857 __isl_give isl_map *isl_map_range_product(
1858 __isl_take isl_map *map1,
1859 __isl_take isl_map *map2);
1860 __isl_give isl_union_map *isl_union_map_range_product(
1861 __isl_take isl_union_map *umap1,
1862 __isl_take isl_union_map *umap2);
1863 __isl_give isl_map *isl_map_product(
1864 __isl_take isl_map *map1,
1865 __isl_take isl_map *map2);
1866 __isl_give isl_union_map *isl_union_map_product(
1867 __isl_take isl_union_map *umap1,
1868 __isl_take isl_union_map *umap2);
1870 The above functions compute the cross product of the given
1871 sets or relations. The domains and ranges of the results
1872 are wrapped maps between domains and ranges of the inputs.
1873 To obtain a ``flat'' product, use the following functions
1876 __isl_give isl_basic_set *isl_basic_set_flat_product(
1877 __isl_take isl_basic_set *bset1,
1878 __isl_take isl_basic_set *bset2);
1879 __isl_give isl_set *isl_set_flat_product(
1880 __isl_take isl_set *set1,
1881 __isl_take isl_set *set2);
1882 __isl_give isl_basic_map *isl_basic_map_flat_product(
1883 __isl_take isl_basic_map *bmap1,
1884 __isl_take isl_basic_map *bmap2);
1885 __isl_give isl_map *isl_map_flat_product(
1886 __isl_take isl_map *map1,
1887 __isl_take isl_map *map2);
1889 =item * Simplification
1891 __isl_give isl_basic_set *isl_basic_set_gist(
1892 __isl_take isl_basic_set *bset,
1893 __isl_take isl_basic_set *context);
1894 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
1895 __isl_take isl_set *context);
1896 __isl_give isl_union_set *isl_union_set_gist(
1897 __isl_take isl_union_set *uset,
1898 __isl_take isl_union_set *context);
1899 __isl_give isl_basic_map *isl_basic_map_gist(
1900 __isl_take isl_basic_map *bmap,
1901 __isl_take isl_basic_map *context);
1902 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
1903 __isl_take isl_map *context);
1904 __isl_give isl_union_map *isl_union_map_gist(
1905 __isl_take isl_union_map *umap,
1906 __isl_take isl_union_map *context);
1908 The gist operation returns a set or relation that has the
1909 same intersection with the context as the input set or relation.
1910 Any implicit equality in the intersection is made explicit in the result,
1911 while all inequalities that are redundant with respect to the intersection
1913 In case of union sets and relations, the gist operation is performed
1918 =head3 Lexicographic Optimization
1920 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
1921 the following functions
1922 compute a set that contains the lexicographic minimum or maximum
1923 of the elements in C<set> (or C<bset>) for those values of the parameters
1924 that satisfy C<dom>.
1925 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
1926 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
1928 In other words, the union of the parameter values
1929 for which the result is non-empty and of C<*empty>
1932 __isl_give isl_set *isl_basic_set_partial_lexmin(
1933 __isl_take isl_basic_set *bset,
1934 __isl_take isl_basic_set *dom,
1935 __isl_give isl_set **empty);
1936 __isl_give isl_set *isl_basic_set_partial_lexmax(
1937 __isl_take isl_basic_set *bset,
1938 __isl_take isl_basic_set *dom,
1939 __isl_give isl_set **empty);
1940 __isl_give isl_set *isl_set_partial_lexmin(
1941 __isl_take isl_set *set, __isl_take isl_set *dom,
1942 __isl_give isl_set **empty);
1943 __isl_give isl_set *isl_set_partial_lexmax(
1944 __isl_take isl_set *set, __isl_take isl_set *dom,
1945 __isl_give isl_set **empty);
1947 Given a (basic) set C<set> (or C<bset>), the following functions simply
1948 return a set containing the lexicographic minimum or maximum
1949 of the elements in C<set> (or C<bset>).
1950 In case of union sets, the optimum is computed per space.
1952 __isl_give isl_set *isl_basic_set_lexmin(
1953 __isl_take isl_basic_set *bset);
1954 __isl_give isl_set *isl_basic_set_lexmax(
1955 __isl_take isl_basic_set *bset);
1956 __isl_give isl_set *isl_set_lexmin(
1957 __isl_take isl_set *set);
1958 __isl_give isl_set *isl_set_lexmax(
1959 __isl_take isl_set *set);
1960 __isl_give isl_union_set *isl_union_set_lexmin(
1961 __isl_take isl_union_set *uset);
1962 __isl_give isl_union_set *isl_union_set_lexmax(
1963 __isl_take isl_union_set *uset);
1965 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
1966 the following functions
1967 compute a relation that maps each element of C<dom>
1968 to the single lexicographic minimum or maximum
1969 of the elements that are associated to that same
1970 element in C<map> (or C<bmap>).
1971 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
1972 that contains the elements in C<dom> that do not map
1973 to any elements in C<map> (or C<bmap>).
1974 In other words, the union of the domain of the result and of C<*empty>
1977 __isl_give isl_map *isl_basic_map_partial_lexmax(
1978 __isl_take isl_basic_map *bmap,
1979 __isl_take isl_basic_set *dom,
1980 __isl_give isl_set **empty);
1981 __isl_give isl_map *isl_basic_map_partial_lexmin(
1982 __isl_take isl_basic_map *bmap,
1983 __isl_take isl_basic_set *dom,
1984 __isl_give isl_set **empty);
1985 __isl_give isl_map *isl_map_partial_lexmax(
1986 __isl_take isl_map *map, __isl_take isl_set *dom,
1987 __isl_give isl_set **empty);
1988 __isl_give isl_map *isl_map_partial_lexmin(
1989 __isl_take isl_map *map, __isl_take isl_set *dom,
1990 __isl_give isl_set **empty);
1992 Given a (basic) map C<map> (or C<bmap>), the following functions simply
1993 return a map mapping each element in the domain of
1994 C<map> (or C<bmap>) to the lexicographic minimum or maximum
1995 of all elements associated to that element.
1996 In case of union relations, the optimum is computed per space.
1998 __isl_give isl_map *isl_basic_map_lexmin(
1999 __isl_take isl_basic_map *bmap);
2000 __isl_give isl_map *isl_basic_map_lexmax(
2001 __isl_take isl_basic_map *bmap);
2002 __isl_give isl_map *isl_map_lexmin(
2003 __isl_take isl_map *map);
2004 __isl_give isl_map *isl_map_lexmax(
2005 __isl_take isl_map *map);
2006 __isl_give isl_union_map *isl_union_map_lexmin(
2007 __isl_take isl_union_map *umap);
2008 __isl_give isl_union_map *isl_union_map_lexmax(
2009 __isl_take isl_union_map *umap);
2013 Lists are defined over several element types, including
2014 C<isl_aff>, C<isl_basic_set> and C<isl_set>.
2015 Here we take lists of C<isl_set>s as an example.
2016 Lists can be created, copied and freed using the following functions.
2018 #include <isl/list.h>
2019 __isl_give isl_set_list *isl_set_list_alloc(
2020 isl_ctx *ctx, int n);
2021 __isl_give isl_set_list *isl_set_list_copy(
2022 __isl_keep isl_set_list *list);
2023 __isl_give isl_set_list *isl_set_list_add(
2024 __isl_take isl_set_list *list,
2025 __isl_take isl_set *el);
2026 void isl_set_list_free(__isl_take isl_set_list *list);
2028 C<isl_set_list_alloc> creates an empty list with a capacity for
2031 Lists can be inspected using the following functions.
2033 #include <isl/list.h>
2034 isl_ctx *isl_set_list_get_ctx(__isl_keep isl_set_list *list);
2035 int isl_set_list_n_set(__isl_keep isl_set_list *list);
2036 __isl_give struct isl_set *isl_set_list_get_set(
2037 __isl_keep isl_set_list *list, int index);
2038 int isl_set_list_foreach(__isl_keep isl_set_list *list,
2039 int (*fn)(__isl_take struct isl_set *el, void *user),
2042 Lists can be printed using
2044 #include <isl/list.h>
2045 __isl_give isl_printer *isl_printer_print_set_list(
2046 __isl_take isl_printer *p,
2047 __isl_keep isl_set_list *list);
2051 Matrices can be created, copied and freed using the following functions.
2053 #include <isl/mat.h>
2054 __isl_give isl_mat *isl_mat_alloc(struct isl_ctx *ctx,
2055 unsigned n_row, unsigned n_col);
2056 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
2057 void isl_mat_free(__isl_take isl_mat *mat);
2059 Note that the elements of a newly created matrix may have arbitrary values.
2060 The elements can be changed and inspected using the following functions.
2062 isl_ctx *isl_mat_get_ctx(__isl_keep isl_mat *mat);
2063 int isl_mat_rows(__isl_keep isl_mat *mat);
2064 int isl_mat_cols(__isl_keep isl_mat *mat);
2065 int isl_mat_get_element(__isl_keep isl_mat *mat,
2066 int row, int col, isl_int *v);
2067 __isl_give isl_mat *isl_mat_set_element(__isl_take isl_mat *mat,
2068 int row, int col, isl_int v);
2069 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
2070 int row, int col, int v);
2072 C<isl_mat_get_element> will return a negative value if anything went wrong.
2073 In that case, the value of C<*v> is undefined.
2075 The following function can be used to compute the (right) inverse
2076 of a matrix, i.e., a matrix such that the product of the original
2077 and the inverse (in that order) is a multiple of the identity matrix.
2078 The input matrix is assumed to be of full row-rank.
2080 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
2082 The following function can be used to compute the (right) kernel
2083 (or null space) of a matrix, i.e., a matrix such that the product of
2084 the original and the kernel (in that order) is the zero matrix.
2086 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
2088 =head2 Quasi Affine Expressions
2090 The zero quasi affine expression can be created using
2092 __isl_give isl_aff *isl_aff_zero(
2093 __isl_take isl_local_space *ls);
2095 Quasi affine expressions can be copied and free using
2097 #include <isl/aff.h>
2098 __isl_give isl_aff *isl_aff_copy(__isl_keep isl_aff *aff);
2099 void *isl_aff_free(__isl_take isl_aff *aff);
2101 A (rational) bound on a dimension can be extracted from an C<isl_constraint>
2102 using the following function. The constraint is required to have
2103 a non-zero coefficient for the specified dimension.
2105 #include <isl/constraint.h>
2106 __isl_give isl_aff *isl_constraint_get_bound(
2107 __isl_keep isl_constraint *constraint,
2108 enum isl_dim_type type, int pos);
2110 Conversely, an equality constraint equating
2111 the affine expression to zero or an inequality constraint enforcing
2112 the affine expression to be non-negative, can be constructed using
2114 __isl_give isl_constraint *isl_equality_from_aff(
2115 __isl_take isl_aff *aff);
2116 __isl_give isl_constraint *isl_inequality_from_aff(
2117 __isl_take isl_aff *aff);
2119 The expression can be inspected using
2121 #include <isl/aff.h>
2122 isl_ctx *isl_aff_get_ctx(__isl_keep isl_aff *aff);
2123 int isl_aff_dim(__isl_keep isl_aff *aff,
2124 enum isl_dim_type type);
2125 __isl_give isl_local_space *isl_aff_get_local_space(
2126 __isl_keep isl_aff *aff);
2127 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
2128 enum isl_dim_type type, unsigned pos);
2129 int isl_aff_get_constant(__isl_keep isl_aff *aff,
2131 int isl_aff_get_coefficient(__isl_keep isl_aff *aff,
2132 enum isl_dim_type type, int pos, isl_int *v);
2133 int isl_aff_get_denominator(__isl_keep isl_aff *aff,
2135 __isl_give isl_div *isl_aff_get_div(
2136 __isl_keep isl_aff *aff, int pos);
2138 It can be modified using
2140 #include <isl/aff.h>
2141 __isl_give isl_aff *isl_aff_set_constant(
2142 __isl_take isl_aff *aff, isl_int v);
2143 __isl_give isl_aff *isl_aff_set_constant_si(
2144 __isl_take isl_aff *aff, int v);
2145 __isl_give isl_aff *isl_aff_set_coefficient(
2146 __isl_take isl_aff *aff,
2147 enum isl_dim_type type, int pos, isl_int v);
2148 __isl_give isl_aff *isl_aff_set_coefficient_si(
2149 __isl_take isl_aff *aff,
2150 enum isl_dim_type type, int pos, int v);
2151 __isl_give isl_aff *isl_aff_set_denominator(
2152 __isl_take isl_aff *aff, isl_int v);
2154 __isl_give isl_aff *isl_aff_add_constant(
2155 __isl_take isl_aff *aff, isl_int v);
2156 __isl_give isl_aff *isl_aff_add_coefficient_si(
2157 __isl_take isl_aff *aff,
2158 enum isl_dim_type type, int pos, int v);
2160 Note that the C<set_constant> and C<set_coefficient> functions
2161 set the I<numerator> of the constant or coefficient, while
2162 C<add_constant> and C<add_coefficient> add an integer value to
2163 the possibly rational constant or coefficient.
2167 #include <isl/aff.h>
2168 __isl_give isl_aff *isl_aff_add(__isl_take isl_aff *aff1,
2169 __isl_take isl_aff *aff2);
2170 __isl_give isl_aff *isl_aff_sub(__isl_take isl_aff *aff1,
2171 __isl_take isl_aff *aff2);
2172 __isl_give isl_aff *isl_aff_neg(__isl_take isl_aff *aff);
2173 __isl_give isl_aff *isl_aff_ceil(__isl_take isl_aff *aff);
2174 __isl_give isl_aff *isl_aff_scale(__isl_take isl_aff *aff,
2176 __isl_give isl_aff *isl_aff_scale_down(__isl_take isl_aff *aff,
2179 An expression can be printed using
2181 #include <isl/aff.h>
2182 __isl_give isl_printer *isl_printer_print_aff(
2183 __isl_take isl_printer *p, __isl_keep isl_aff *aff);
2187 Points are elements of a set. They can be used to construct
2188 simple sets (boxes) or they can be used to represent the
2189 individual elements of a set.
2190 The zero point (the origin) can be created using
2192 __isl_give isl_point *isl_point_zero(__isl_take isl_dim *dim);
2194 The coordinates of a point can be inspected, set and changed
2197 void isl_point_get_coordinate(__isl_keep isl_point *pnt,
2198 enum isl_dim_type type, int pos, isl_int *v);
2199 __isl_give isl_point *isl_point_set_coordinate(
2200 __isl_take isl_point *pnt,
2201 enum isl_dim_type type, int pos, isl_int v);
2203 __isl_give isl_point *isl_point_add_ui(
2204 __isl_take isl_point *pnt,
2205 enum isl_dim_type type, int pos, unsigned val);
2206 __isl_give isl_point *isl_point_sub_ui(
2207 __isl_take isl_point *pnt,
2208 enum isl_dim_type type, int pos, unsigned val);
2210 Points can be copied or freed using
2212 __isl_give isl_point *isl_point_copy(
2213 __isl_keep isl_point *pnt);
2214 void isl_point_free(__isl_take isl_point *pnt);
2216 A singleton set can be created from a point using
2218 __isl_give isl_basic_set *isl_basic_set_from_point(
2219 __isl_take isl_point *pnt);
2220 __isl_give isl_set *isl_set_from_point(
2221 __isl_take isl_point *pnt);
2223 and a box can be created from two opposite extremal points using
2225 __isl_give isl_basic_set *isl_basic_set_box_from_points(
2226 __isl_take isl_point *pnt1,
2227 __isl_take isl_point *pnt2);
2228 __isl_give isl_set *isl_set_box_from_points(
2229 __isl_take isl_point *pnt1,
2230 __isl_take isl_point *pnt2);
2232 All elements of a B<bounded> (union) set can be enumerated using
2233 the following functions.
2235 int isl_set_foreach_point(__isl_keep isl_set *set,
2236 int (*fn)(__isl_take isl_point *pnt, void *user),
2238 int isl_union_set_foreach_point(__isl_keep isl_union_set *uset,
2239 int (*fn)(__isl_take isl_point *pnt, void *user),
2242 The function C<fn> is called for each integer point in
2243 C<set> with as second argument the last argument of
2244 the C<isl_set_foreach_point> call. The function C<fn>
2245 should return C<0> on success and C<-1> on failure.
2246 In the latter case, C<isl_set_foreach_point> will stop
2247 enumerating and return C<-1> as well.
2248 If the enumeration is performed successfully and to completion,
2249 then C<isl_set_foreach_point> returns C<0>.
2251 To obtain a single point of a (basic) set, use
2253 __isl_give isl_point *isl_basic_set_sample_point(
2254 __isl_take isl_basic_set *bset);
2255 __isl_give isl_point *isl_set_sample_point(
2256 __isl_take isl_set *set);
2258 If C<set> does not contain any (integer) points, then the
2259 resulting point will be ``void'', a property that can be
2262 int isl_point_is_void(__isl_keep isl_point *pnt);
2264 =head2 Piecewise Quasipolynomials
2266 A piecewise quasipolynomial is a particular kind of function that maps
2267 a parametric point to a rational value.
2268 More specifically, a quasipolynomial is a polynomial expression in greatest
2269 integer parts of affine expressions of parameters and variables.
2270 A piecewise quasipolynomial is a subdivision of a given parametric
2271 domain into disjoint cells with a quasipolynomial associated to
2272 each cell. The value of the piecewise quasipolynomial at a given
2273 point is the value of the quasipolynomial associated to the cell
2274 that contains the point. Outside of the union of cells,
2275 the value is assumed to be zero.
2276 For example, the piecewise quasipolynomial
2278 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
2280 maps C<x> to C<1 + n - x> for values of C<x> between C<0> and C<n>.
2281 A given piecewise quasipolynomial has a fixed domain dimension.
2282 Union piecewise quasipolynomials are used to contain piecewise quasipolynomials
2283 defined over different domains.
2284 Piecewise quasipolynomials are mainly used by the C<barvinok>
2285 library for representing the number of elements in a parametric set or map.
2286 For example, the piecewise quasipolynomial above represents
2287 the number of points in the map
2289 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
2291 =head3 Printing (Piecewise) Quasipolynomials
2293 Quasipolynomials and piecewise quasipolynomials can be printed
2294 using the following functions.
2296 __isl_give isl_printer *isl_printer_print_qpolynomial(
2297 __isl_take isl_printer *p,
2298 __isl_keep isl_qpolynomial *qp);
2300 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
2301 __isl_take isl_printer *p,
2302 __isl_keep isl_pw_qpolynomial *pwqp);
2304 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
2305 __isl_take isl_printer *p,
2306 __isl_keep isl_union_pw_qpolynomial *upwqp);
2308 The output format of the printer
2309 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
2310 For C<isl_printer_print_union_pw_qpolynomial>, only C<ISL_FORMAT_ISL>
2312 In case of printing in C<ISL_FORMAT_C>, the user may want
2313 to set the names of all dimensions
2315 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
2316 __isl_take isl_qpolynomial *qp,
2317 enum isl_dim_type type, unsigned pos,
2319 __isl_give isl_pw_qpolynomial *
2320 isl_pw_qpolynomial_set_dim_name(
2321 __isl_take isl_pw_qpolynomial *pwqp,
2322 enum isl_dim_type type, unsigned pos,
2325 =head3 Creating New (Piecewise) Quasipolynomials
2327 Some simple quasipolynomials can be created using the following functions.
2328 More complicated quasipolynomials can be created by applying
2329 operations such as addition and multiplication
2330 on the resulting quasipolynomials
2332 __isl_give isl_qpolynomial *isl_qpolynomial_zero(
2333 __isl_take isl_dim *dim);
2334 __isl_give isl_qpolynomial *isl_qpolynomial_one(
2335 __isl_take isl_dim *dim);
2336 __isl_give isl_qpolynomial *isl_qpolynomial_infty(
2337 __isl_take isl_dim *dim);
2338 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty(
2339 __isl_take isl_dim *dim);
2340 __isl_give isl_qpolynomial *isl_qpolynomial_nan(
2341 __isl_take isl_dim *dim);
2342 __isl_give isl_qpolynomial *isl_qpolynomial_rat_cst(
2343 __isl_take isl_dim *dim,
2344 const isl_int n, const isl_int d);
2345 __isl_give isl_qpolynomial *isl_qpolynomial_div(
2346 __isl_take isl_div *div);
2347 __isl_give isl_qpolynomial *isl_qpolynomial_var(
2348 __isl_take isl_dim *dim,
2349 enum isl_dim_type type, unsigned pos);
2350 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(
2351 __isl_take isl_aff *aff);
2353 The zero piecewise quasipolynomial or a piecewise quasipolynomial
2354 with a single cell can be created using the following functions.
2355 Multiple of these single cell piecewise quasipolynomials can
2356 be combined to create more complicated piecewise quasipolynomials.
2358 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
2359 __isl_take isl_dim *dim);
2360 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
2361 __isl_take isl_set *set,
2362 __isl_take isl_qpolynomial *qp);
2364 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_zero(
2365 __isl_take isl_dim *dim);
2366 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_from_pw_qpolynomial(
2367 __isl_take isl_pw_qpolynomial *pwqp);
2368 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add_pw_qpolynomial(
2369 __isl_take isl_union_pw_qpolynomial *upwqp,
2370 __isl_take isl_pw_qpolynomial *pwqp);
2372 Quasipolynomials can be copied and freed again using the following
2375 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
2376 __isl_keep isl_qpolynomial *qp);
2377 void isl_qpolynomial_free(__isl_take isl_qpolynomial *qp);
2379 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
2380 __isl_keep isl_pw_qpolynomial *pwqp);
2381 void isl_pw_qpolynomial_free(
2382 __isl_take isl_pw_qpolynomial *pwqp);
2384 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_copy(
2385 __isl_keep isl_union_pw_qpolynomial *upwqp);
2386 void isl_union_pw_qpolynomial_free(
2387 __isl_take isl_union_pw_qpolynomial *upwqp);
2389 =head3 Inspecting (Piecewise) Quasipolynomials
2391 To iterate over all piecewise quasipolynomials in a union
2392 piecewise quasipolynomial, use the following function
2394 int isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
2395 __isl_keep isl_union_pw_qpolynomial *upwqp,
2396 int (*fn)(__isl_take isl_pw_qpolynomial *pwqp, void *user),
2399 To extract the piecewise quasipolynomial from a union with a given dimension
2402 __isl_give isl_pw_qpolynomial *
2403 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
2404 __isl_keep isl_union_pw_qpolynomial *upwqp,
2405 __isl_take isl_dim *dim);
2407 To iterate over the cells in a piecewise quasipolynomial,
2408 use either of the following two functions
2410 int isl_pw_qpolynomial_foreach_piece(
2411 __isl_keep isl_pw_qpolynomial *pwqp,
2412 int (*fn)(__isl_take isl_set *set,
2413 __isl_take isl_qpolynomial *qp,
2414 void *user), void *user);
2415 int isl_pw_qpolynomial_foreach_lifted_piece(
2416 __isl_keep isl_pw_qpolynomial *pwqp,
2417 int (*fn)(__isl_take isl_set *set,
2418 __isl_take isl_qpolynomial *qp,
2419 void *user), void *user);
2421 As usual, the function C<fn> should return C<0> on success
2422 and C<-1> on failure. The difference between
2423 C<isl_pw_qpolynomial_foreach_piece> and
2424 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
2425 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
2426 compute unique representations for all existentially quantified
2427 variables and then turn these existentially quantified variables
2428 into extra set variables, adapting the associated quasipolynomial
2429 accordingly. This means that the C<set> passed to C<fn>
2430 will not have any existentially quantified variables, but that
2431 the dimensions of the sets may be different for different
2432 invocations of C<fn>.
2434 To iterate over all terms in a quasipolynomial,
2437 int isl_qpolynomial_foreach_term(
2438 __isl_keep isl_qpolynomial *qp,
2439 int (*fn)(__isl_take isl_term *term,
2440 void *user), void *user);
2442 The terms themselves can be inspected and freed using
2445 unsigned isl_term_dim(__isl_keep isl_term *term,
2446 enum isl_dim_type type);
2447 void isl_term_get_num(__isl_keep isl_term *term,
2449 void isl_term_get_den(__isl_keep isl_term *term,
2451 int isl_term_get_exp(__isl_keep isl_term *term,
2452 enum isl_dim_type type, unsigned pos);
2453 __isl_give isl_div *isl_term_get_div(
2454 __isl_keep isl_term *term, unsigned pos);
2455 void isl_term_free(__isl_take isl_term *term);
2457 Each term is a product of parameters, set variables and
2458 integer divisions. The function C<isl_term_get_exp>
2459 returns the exponent of a given dimensions in the given term.
2460 The C<isl_int>s in the arguments of C<isl_term_get_num>
2461 and C<isl_term_get_den> need to have been initialized
2462 using C<isl_int_init> before calling these functions.
2464 =head3 Properties of (Piecewise) Quasipolynomials
2466 To check whether a quasipolynomial is actually a constant,
2467 use the following function.
2469 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp,
2470 isl_int *n, isl_int *d);
2472 If C<qp> is a constant and if C<n> and C<d> are not C<NULL>
2473 then the numerator and denominator of the constant
2474 are returned in C<*n> and C<*d>, respectively.
2476 =head3 Operations on (Piecewise) Quasipolynomials
2478 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
2479 __isl_take isl_qpolynomial *qp);
2480 __isl_give isl_qpolynomial *isl_qpolynomial_add(
2481 __isl_take isl_qpolynomial *qp1,
2482 __isl_take isl_qpolynomial *qp2);
2483 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
2484 __isl_take isl_qpolynomial *qp1,
2485 __isl_take isl_qpolynomial *qp2);
2486 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
2487 __isl_take isl_qpolynomial *qp1,
2488 __isl_take isl_qpolynomial *qp2);
2489 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
2490 __isl_take isl_qpolynomial *qp, unsigned exponent);
2492 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
2493 __isl_take isl_pw_qpolynomial *pwqp1,
2494 __isl_take isl_pw_qpolynomial *pwqp2);
2495 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
2496 __isl_take isl_pw_qpolynomial *pwqp1,
2497 __isl_take isl_pw_qpolynomial *pwqp2);
2498 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
2499 __isl_take isl_pw_qpolynomial *pwqp1,
2500 __isl_take isl_pw_qpolynomial *pwqp2);
2501 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
2502 __isl_take isl_pw_qpolynomial *pwqp);
2503 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
2504 __isl_take isl_pw_qpolynomial *pwqp1,
2505 __isl_take isl_pw_qpolynomial *pwqp2);
2507 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
2508 __isl_take isl_union_pw_qpolynomial *upwqp1,
2509 __isl_take isl_union_pw_qpolynomial *upwqp2);
2510 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
2511 __isl_take isl_union_pw_qpolynomial *upwqp1,
2512 __isl_take isl_union_pw_qpolynomial *upwqp2);
2513 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
2514 __isl_take isl_union_pw_qpolynomial *upwqp1,
2515 __isl_take isl_union_pw_qpolynomial *upwqp2);
2517 __isl_give isl_qpolynomial *isl_pw_qpolynomial_eval(
2518 __isl_take isl_pw_qpolynomial *pwqp,
2519 __isl_take isl_point *pnt);
2521 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_eval(
2522 __isl_take isl_union_pw_qpolynomial *upwqp,
2523 __isl_take isl_point *pnt);
2525 __isl_give isl_set *isl_pw_qpolynomial_domain(
2526 __isl_take isl_pw_qpolynomial *pwqp);
2527 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_domain(
2528 __isl_take isl_pw_qpolynomial *pwpq,
2529 __isl_take isl_set *set);
2531 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
2532 __isl_take isl_union_pw_qpolynomial *upwqp);
2533 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_intersect_domain(
2534 __isl_take isl_union_pw_qpolynomial *upwpq,
2535 __isl_take isl_union_set *uset);
2537 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
2538 __isl_take isl_qpolynomial *qp,
2539 __isl_take isl_dim *model);
2541 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_coalesce(
2542 __isl_take isl_union_pw_qpolynomial *upwqp);
2544 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
2545 __isl_take isl_qpolynomial *qp,
2546 __isl_take isl_set *context);
2548 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
2549 __isl_take isl_pw_qpolynomial *pwqp,
2550 __isl_take isl_set *context);
2552 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
2553 __isl_take isl_union_pw_qpolynomial *upwqp,
2554 __isl_take isl_union_set *context);
2556 The gist operation applies the gist operation to each of
2557 the cells in the domain of the input piecewise quasipolynomial.
2558 The context is also exploited
2559 to simplify the quasipolynomials associated to each cell.
2561 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
2562 __isl_take isl_pw_qpolynomial *pwqp, int sign);
2563 __isl_give isl_union_pw_qpolynomial *
2564 isl_union_pw_qpolynomial_to_polynomial(
2565 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
2567 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
2568 the polynomial will be an overapproximation. If C<sign> is negative,
2569 it will be an underapproximation. If C<sign> is zero, the approximation
2570 will lie somewhere in between.
2572 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
2574 A piecewise quasipolynomial reduction is a piecewise
2575 reduction (or fold) of quasipolynomials.
2576 In particular, the reduction can be maximum or a minimum.
2577 The objects are mainly used to represent the result of
2578 an upper or lower bound on a quasipolynomial over its domain,
2579 i.e., as the result of the following function.
2581 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_bound(
2582 __isl_take isl_pw_qpolynomial *pwqp,
2583 enum isl_fold type, int *tight);
2585 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_bound(
2586 __isl_take isl_union_pw_qpolynomial *upwqp,
2587 enum isl_fold type, int *tight);
2589 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
2590 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
2591 is the returned bound is known be tight, i.e., for each value
2592 of the parameters there is at least
2593 one element in the domain that reaches the bound.
2594 If the domain of C<pwqp> is not wrapping, then the bound is computed
2595 over all elements in that domain and the result has a purely parametric
2596 domain. If the domain of C<pwqp> is wrapping, then the bound is
2597 computed over the range of the wrapped relation. The domain of the
2598 wrapped relation becomes the domain of the result.
2600 A (piecewise) quasipolynomial reduction can be copied or freed using the
2601 following functions.
2603 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_copy(
2604 __isl_keep isl_qpolynomial_fold *fold);
2605 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_copy(
2606 __isl_keep isl_pw_qpolynomial_fold *pwf);
2607 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_copy(
2608 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
2609 void isl_qpolynomial_fold_free(
2610 __isl_take isl_qpolynomial_fold *fold);
2611 void isl_pw_qpolynomial_fold_free(
2612 __isl_take isl_pw_qpolynomial_fold *pwf);
2613 void isl_union_pw_qpolynomial_fold_free(
2614 __isl_take isl_union_pw_qpolynomial_fold *upwf);
2616 =head3 Printing Piecewise Quasipolynomial Reductions
2618 Piecewise quasipolynomial reductions can be printed
2619 using the following function.
2621 __isl_give isl_printer *isl_printer_print_pw_qpolynomial_fold(
2622 __isl_take isl_printer *p,
2623 __isl_keep isl_pw_qpolynomial_fold *pwf);
2624 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial_fold(
2625 __isl_take isl_printer *p,
2626 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
2628 For C<isl_printer_print_pw_qpolynomial_fold>,
2629 output format of the printer
2630 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
2631 For C<isl_printer_print_union_pw_qpolynomial_fold>,
2632 output format of the printer
2633 needs to be set to C<ISL_FORMAT_ISL>.
2634 In case of printing in C<ISL_FORMAT_C>, the user may want
2635 to set the names of all dimensions
2637 __isl_give isl_pw_qpolynomial_fold *
2638 isl_pw_qpolynomial_fold_set_dim_name(
2639 __isl_take isl_pw_qpolynomial_fold *pwf,
2640 enum isl_dim_type type, unsigned pos,
2643 =head3 Inspecting (Piecewise) Quasipolynomial Reductions
2645 To iterate over all piecewise quasipolynomial reductions in a union
2646 piecewise quasipolynomial reduction, use the following function
2648 int isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
2649 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
2650 int (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
2651 void *user), void *user);
2653 To iterate over the cells in a piecewise quasipolynomial reduction,
2654 use either of the following two functions
2656 int isl_pw_qpolynomial_fold_foreach_piece(
2657 __isl_keep isl_pw_qpolynomial_fold *pwf,
2658 int (*fn)(__isl_take isl_set *set,
2659 __isl_take isl_qpolynomial_fold *fold,
2660 void *user), void *user);
2661 int isl_pw_qpolynomial_fold_foreach_lifted_piece(
2662 __isl_keep isl_pw_qpolynomial_fold *pwf,
2663 int (*fn)(__isl_take isl_set *set,
2664 __isl_take isl_qpolynomial_fold *fold,
2665 void *user), void *user);
2667 See L<Inspecting (Piecewise) Quasipolynomials> for an explanation
2668 of the difference between these two functions.
2670 To iterate over all quasipolynomials in a reduction, use
2672 int isl_qpolynomial_fold_foreach_qpolynomial(
2673 __isl_keep isl_qpolynomial_fold *fold,
2674 int (*fn)(__isl_take isl_qpolynomial *qp,
2675 void *user), void *user);
2677 =head3 Operations on Piecewise Quasipolynomial Reductions
2679 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
2680 __isl_take isl_pw_qpolynomial_fold *pwf1,
2681 __isl_take isl_pw_qpolynomial_fold *pwf2);
2683 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
2684 __isl_take isl_pw_qpolynomial_fold *pwf1,
2685 __isl_take isl_pw_qpolynomial_fold *pwf2);
2687 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold(
2688 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
2689 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
2691 __isl_give isl_qpolynomial *isl_pw_qpolynomial_fold_eval(
2692 __isl_take isl_pw_qpolynomial_fold *pwf,
2693 __isl_take isl_point *pnt);
2695 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_fold_eval(
2696 __isl_take isl_union_pw_qpolynomial_fold *upwf,
2697 __isl_take isl_point *pnt);
2699 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
2700 __isl_take isl_union_pw_qpolynomial_fold *upwf);
2701 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_intersect_domain(
2702 __isl_take isl_union_pw_qpolynomial_fold *upwf,
2703 __isl_take isl_union_set *uset);
2705 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_coalesce(
2706 __isl_take isl_pw_qpolynomial_fold *pwf);
2708 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_coalesce(
2709 __isl_take isl_union_pw_qpolynomial_fold *upwf);
2711 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist(
2712 __isl_take isl_pw_qpolynomial_fold *pwf,
2713 __isl_take isl_set *context);
2715 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_gist(
2716 __isl_take isl_union_pw_qpolynomial_fold *upwf,
2717 __isl_take isl_union_set *context);
2719 The gist operation applies the gist operation to each of
2720 the cells in the domain of the input piecewise quasipolynomial reduction.
2721 In future, the operation will also exploit the context
2722 to simplify the quasipolynomial reductions associated to each cell.
2724 __isl_give isl_pw_qpolynomial_fold *
2725 isl_set_apply_pw_qpolynomial_fold(
2726 __isl_take isl_set *set,
2727 __isl_take isl_pw_qpolynomial_fold *pwf,
2729 __isl_give isl_pw_qpolynomial_fold *
2730 isl_map_apply_pw_qpolynomial_fold(
2731 __isl_take isl_map *map,
2732 __isl_take isl_pw_qpolynomial_fold *pwf,
2734 __isl_give isl_union_pw_qpolynomial_fold *
2735 isl_union_set_apply_union_pw_qpolynomial_fold(
2736 __isl_take isl_union_set *uset,
2737 __isl_take isl_union_pw_qpolynomial_fold *upwf,
2739 __isl_give isl_union_pw_qpolynomial_fold *
2740 isl_union_map_apply_union_pw_qpolynomial_fold(
2741 __isl_take isl_union_map *umap,
2742 __isl_take isl_union_pw_qpolynomial_fold *upwf,
2745 The functions taking a map
2746 compose the given map with the given piecewise quasipolynomial reduction.
2747 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
2748 over all elements in the intersection of the range of the map
2749 and the domain of the piecewise quasipolynomial reduction
2750 as a function of an element in the domain of the map.
2751 The functions taking a set compute a bound over all elements in the
2752 intersection of the set and the domain of the
2753 piecewise quasipolynomial reduction.
2755 =head2 Dependence Analysis
2757 C<isl> contains specialized functionality for performing
2758 array dataflow analysis. That is, given a I<sink> access relation
2759 and a collection of possible I<source> access relations,
2760 C<isl> can compute relations that describe
2761 for each iteration of the sink access, which iteration
2762 of which of the source access relations was the last
2763 to access the same data element before the given iteration
2765 To compute standard flow dependences, the sink should be
2766 a read, while the sources should be writes.
2767 If any of the source accesses are marked as being I<may>
2768 accesses, then there will be a dependence to the last
2769 I<must> access B<and> to any I<may> access that follows
2770 this last I<must> access.
2771 In particular, if I<all> sources are I<may> accesses,
2772 then memory based dependence analysis is performed.
2773 If, on the other hand, all sources are I<must> accesses,
2774 then value based dependence analysis is performed.
2776 #include <isl/flow.h>
2778 typedef int (*isl_access_level_before)(void *first, void *second);
2780 __isl_give isl_access_info *isl_access_info_alloc(
2781 __isl_take isl_map *sink,
2782 void *sink_user, isl_access_level_before fn,
2784 __isl_give isl_access_info *isl_access_info_add_source(
2785 __isl_take isl_access_info *acc,
2786 __isl_take isl_map *source, int must,
2788 void isl_access_info_free(__isl_take isl_access_info *acc);
2790 __isl_give isl_flow *isl_access_info_compute_flow(
2791 __isl_take isl_access_info *acc);
2793 int isl_flow_foreach(__isl_keep isl_flow *deps,
2794 int (*fn)(__isl_take isl_map *dep, int must,
2795 void *dep_user, void *user),
2797 __isl_give isl_map *isl_flow_get_no_source(
2798 __isl_keep isl_flow *deps, int must);
2799 void isl_flow_free(__isl_take isl_flow *deps);
2801 The function C<isl_access_info_compute_flow> performs the actual
2802 dependence analysis. The other functions are used to construct
2803 the input for this function or to read off the output.
2805 The input is collected in an C<isl_access_info>, which can
2806 be created through a call to C<isl_access_info_alloc>.
2807 The arguments to this functions are the sink access relation
2808 C<sink>, a token C<sink_user> used to identify the sink
2809 access to the user, a callback function for specifying the
2810 relative order of source and sink accesses, and the number
2811 of source access relations that will be added.
2812 The callback function has type C<int (*)(void *first, void *second)>.
2813 The function is called with two user supplied tokens identifying
2814 either a source or the sink and it should return the shared nesting
2815 level and the relative order of the two accesses.
2816 In particular, let I<n> be the number of loops shared by
2817 the two accesses. If C<first> precedes C<second> textually,
2818 then the function should return I<2 * n + 1>; otherwise,
2819 it should return I<2 * n>.
2820 The sources can be added to the C<isl_access_info> by performing
2821 (at most) C<max_source> calls to C<isl_access_info_add_source>.
2822 C<must> indicates whether the source is a I<must> access
2823 or a I<may> access. Note that a multi-valued access relation
2824 should only be marked I<must> if every iteration in the domain
2825 of the relation accesses I<all> elements in its image.
2826 The C<source_user> token is again used to identify
2827 the source access. The range of the source access relation
2828 C<source> should have the same dimension as the range
2829 of the sink access relation.
2830 The C<isl_access_info_free> function should usually not be
2831 called explicitly, because it is called implicitly by
2832 C<isl_access_info_compute_flow>.
2834 The result of the dependence analysis is collected in an
2835 C<isl_flow>. There may be elements of
2836 the sink access for which no preceding source access could be
2837 found or for which all preceding sources are I<may> accesses.
2838 The relations containing these elements can be obtained through
2839 calls to C<isl_flow_get_no_source>, the first with C<must> set
2840 and the second with C<must> unset.
2841 In the case of standard flow dependence analysis,
2842 with the sink a read and the sources I<must> writes,
2843 the first relation corresponds to the reads from uninitialized
2844 array elements and the second relation is empty.
2845 The actual flow dependences can be extracted using
2846 C<isl_flow_foreach>. This function will call the user-specified
2847 callback function C<fn> for each B<non-empty> dependence between
2848 a source and the sink. The callback function is called
2849 with four arguments, the actual flow dependence relation
2850 mapping source iterations to sink iterations, a boolean that
2851 indicates whether it is a I<must> or I<may> dependence, a token
2852 identifying the source and an additional C<void *> with value
2853 equal to the third argument of the C<isl_flow_foreach> call.
2854 A dependence is marked I<must> if it originates from a I<must>
2855 source and if it is not followed by any I<may> sources.
2857 After finishing with an C<isl_flow>, the user should call
2858 C<isl_flow_free> to free all associated memory.
2860 A higher-level interface to dependence analysis is provided
2861 by the following function.
2863 #include <isl/flow.h>
2865 int isl_union_map_compute_flow(__isl_take isl_union_map *sink,
2866 __isl_take isl_union_map *must_source,
2867 __isl_take isl_union_map *may_source,
2868 __isl_take isl_union_map *schedule,
2869 __isl_give isl_union_map **must_dep,
2870 __isl_give isl_union_map **may_dep,
2871 __isl_give isl_union_map **must_no_source,
2872 __isl_give isl_union_map **may_no_source);
2874 The arrays are identified by the tuple names of the ranges
2875 of the accesses. The iteration domains by the tuple names
2876 of the domains of the accesses and of the schedule.
2877 The relative order of the iteration domains is given by the
2878 schedule. The relations returned through C<must_no_source>
2879 and C<may_no_source> are subsets of C<sink>.
2880 Any of C<must_dep>, C<may_dep>, C<must_no_source>
2881 or C<may_no_source> may be C<NULL>, but a C<NULL> value for
2882 any of the other arguments is treated as an error.
2886 B<The functionality described in this section is fairly new
2887 and may be subject to change.>
2889 The following function can be used to compute a schedule
2890 for a union of domains. The generated schedule respects
2891 all C<validity> dependences. That is, all dependence distances
2892 over these dependences in the scheduled space are lexicographically
2893 positive. The generated schedule schedule also tries to minimize
2894 the dependence distances over C<proximity> dependences.
2895 Moreover, it tries to obtain sequences (bands) of schedule dimensions
2896 for groups of domains where the dependence distances have only
2897 non-negative values.
2898 The algorithm used to construct the schedule is similar to that
2901 #include <isl/schedule.h>
2902 __isl_give isl_schedule *isl_union_set_compute_schedule(
2903 __isl_take isl_union_set *domain,
2904 __isl_take isl_union_map *validity,
2905 __isl_take isl_union_map *proximity);
2906 void *isl_schedule_free(__isl_take isl_schedule *sched);
2908 A mapping from the domains to the scheduled space can be obtained
2909 from an C<isl_schedule> using the following function.
2911 __isl_give isl_union_map *isl_schedule_get_map(
2912 __isl_keep isl_schedule *sched);
2914 This mapping can also be obtained in pieces using the following functions.
2916 int isl_schedule_n_band(__isl_keep isl_schedule *sched);
2917 __isl_give isl_union_map *isl_schedule_get_band(
2918 __isl_keep isl_schedule *sched, unsigned band);
2920 C<isl_schedule_n_band> returns the maximal number of bands.
2921 C<isl_schedule_get_band> returns a union of mappings from a domain to
2922 the band of consecutive schedule dimensions with the given sequence
2923 number for that domain. Bands with the same sequence number but for
2924 different domains may be completely unrelated.
2925 Within a band, the corresponding coordinates of the distance vectors
2926 are all non-negative, assuming that the coordinates for all previous
2929 =head2 Parametric Vertex Enumeration
2931 The parametric vertex enumeration described in this section
2932 is mainly intended to be used internally and by the C<barvinok>
2935 #include <isl/vertices.h>
2936 __isl_give isl_vertices *isl_basic_set_compute_vertices(
2937 __isl_keep isl_basic_set *bset);
2939 The function C<isl_basic_set_compute_vertices> performs the
2940 actual computation of the parametric vertices and the chamber
2941 decomposition and store the result in an C<isl_vertices> object.
2942 This information can be queried by either iterating over all
2943 the vertices or iterating over all the chambers or cells
2944 and then iterating over all vertices that are active on the chamber.
2946 int isl_vertices_foreach_vertex(
2947 __isl_keep isl_vertices *vertices,
2948 int (*fn)(__isl_take isl_vertex *vertex, void *user),
2951 int isl_vertices_foreach_cell(
2952 __isl_keep isl_vertices *vertices,
2953 int (*fn)(__isl_take isl_cell *cell, void *user),
2955 int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
2956 int (*fn)(__isl_take isl_vertex *vertex, void *user),
2959 Other operations that can be performed on an C<isl_vertices> object are
2962 isl_ctx *isl_vertices_get_ctx(
2963 __isl_keep isl_vertices *vertices);
2964 int isl_vertices_get_n_vertices(
2965 __isl_keep isl_vertices *vertices);
2966 void isl_vertices_free(__isl_take isl_vertices *vertices);
2968 Vertices can be inspected and destroyed using the following functions.
2970 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
2971 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
2972 __isl_give isl_basic_set *isl_vertex_get_domain(
2973 __isl_keep isl_vertex *vertex);
2974 __isl_give isl_basic_set *isl_vertex_get_expr(
2975 __isl_keep isl_vertex *vertex);
2976 void isl_vertex_free(__isl_take isl_vertex *vertex);
2978 C<isl_vertex_get_expr> returns a singleton parametric set describing
2979 the vertex, while C<isl_vertex_get_domain> returns the activity domain
2981 Note that C<isl_vertex_get_domain> and C<isl_vertex_get_expr> return
2982 B<rational> basic sets, so they should mainly be used for inspection
2983 and should not be mixed with integer sets.
2985 Chambers can be inspected and destroyed using the following functions.
2987 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
2988 __isl_give isl_basic_set *isl_cell_get_domain(
2989 __isl_keep isl_cell *cell);
2990 void isl_cell_free(__isl_take isl_cell *cell);
2994 Although C<isl> is mainly meant to be used as a library,
2995 it also contains some basic applications that use some
2996 of the functionality of C<isl>.
2997 The input may be specified in either the L<isl format>
2998 or the L<PolyLib format>.
3000 =head2 C<isl_polyhedron_sample>
3002 C<isl_polyhedron_sample> takes a polyhedron as input and prints
3003 an integer element of the polyhedron, if there is any.
3004 The first column in the output is the denominator and is always
3005 equal to 1. If the polyhedron contains no integer points,
3006 then a vector of length zero is printed.
3010 C<isl_pip> takes the same input as the C<example> program
3011 from the C<piplib> distribution, i.e., a set of constraints
3012 on the parameters, a line containing only -1 and finally a set
3013 of constraints on a parametric polyhedron.
3014 The coefficients of the parameters appear in the last columns
3015 (but before the final constant column).
3016 The output is the lexicographic minimum of the parametric polyhedron.
3017 As C<isl> currently does not have its own output format, the output
3018 is just a dump of the internal state.
3020 =head2 C<isl_polyhedron_minimize>
3022 C<isl_polyhedron_minimize> computes the minimum of some linear
3023 or affine objective function over the integer points in a polyhedron.
3024 If an affine objective function
3025 is given, then the constant should appear in the last column.
3027 =head2 C<isl_polytope_scan>
3029 Given a polytope, C<isl_polytope_scan> prints
3030 all integer points in the polytope.